text: Another noteworthy feature is the "jewel save". The jewels that power the reflector device can be clicked to place a mark on the divergence map, which consumes the jewel. The divergence map can later be opened and players can return to the mark instantly, regaining the jewel. If a jewel save is made before a story branch point, players can explore one scenario then quickly return and explore an alternative. This feature is akin to saving or loading the game. Key items can be carried from one world to another through the jewel save.


title: YU-NO: A Girl Who Chants Love at the Bound of this World

text: After the epilogue, a new feature called "Start with Best Equipment" is added. This essentially returns all jewels placed on the ADMS back to the reflector device and sends the player back to the start of the branch, with all 19 items in their inventory. Their map progress is also saved.


text: Sections at the beginning and end of the game have a more traditional visual-novel-style gameplay, in which players choose commands like "Look" or "Speak" from a menu. There are no branching paths in these sections and the Reflector Device cannot be used until they end.


text: The game begins with a linear prologue which introduces the setting and characters, taking place during a couple of days. The player controls Takuya Arima, a student in the fictional Japanese city Sakaimachi. Takuya had a frictive relationship with his historian father Koudai Arima, who has been declared dead after months of disappearance. Takuya barely remembers his biological mother Keiko Arima who had died when he was very young, and he now lives with his stepmother Ayumi Arima. Ayumi is still grieving the loss of Koudai after only six months of marriage and is increasingly busy with work. Eriko Takeda is Takuya's new homeroom teacher and school nurse from abroad; she has become addicted to smoking and, unfamiliar with Japanese standards, took up Takuya's advice to dress skimpily. He meets Koudai's research partner and Sakaimachi Academy's headmaster Kouzou Ryuuzouji, who requests Koudai's belongings. His secretary is Mitsuki Ichijou, a former teacher and lover of Takuya. Some other students at Takuya's school include recent transfer student Kanna Hatano, the mayor's daughter Mio Shimazu, and Masakatsu Yuuki. Takuya meets Ayumi's underling Hideo Toyotomi, whom he takes an instant disliking to.


text: On a nearby beach, there is a tower-like rock formation going by the names Sword Cape and Triangle Mountain, at the foot of which stand two rocks dated as 8000 years old with unknown, 400 years old writing on them. Geo Technics, the company Ayumi works for, is occupying the beach as a construction survey site, but the workers are constantly injured by inexplicable lightning strikes. Kanna habitually warns people to stay away from the area.


text: One evening Takuya receives a package containing an incomplete letter from Koudai and a small otherworldly device with several slots, some fitted with round jewels. The letter talks about Koudai's theory of history and multiple timelines, tells that Koudai has departed elsewhere rather than having died, that the device (known as the Reflector Device) can be used to turn back time, and that Takuya should find the missing jewels and afterwards come to Sword Cape 10 PM that night to meet somebody. Takuya arrives (without all the jewels) and encounters there a naked blonde woman, who upon awakening kisses him, dies and vanishes from existence. Ryuuzouji and Ayumi arrive; Ryuuzouji demands at gunpoint Takuya to hand over the Reflector Device, but a sudden spacetime distortion shifts Takuya to an alternate timeline where he's alone at Sword Cape.


text: At this point the Reflector Device becomes usable and the story starts to split, each main route focusing on a different female character. Jewels are found at various points throughout. A phenomenon known as Chaos Correction will loop Takuya to the beginning of this gameplay section after about two days of in-story time, that is, at the end of a route; his items but not memories are retained whenever crossing time.


text: After initial confusion, Takuya returns to sleep at home. The next day, he discovers that Ayumi is all right; however, neither she nor Ryuuzouji remember the confrontation from the night before. By this time Koudai's study, locked the night before, has been emptied and its contents delivered to Ryuuzouji.


text: The key allows Takuya to enter the study before it's emptied, finding therein a journal by Koudai completing the letter from earlier. It talks about Koudai's life and how he met Keiko. Originally named Kaytia, she was the oldest living Sakaimachi inhabitant at the time but youthful in appearance with blonde hair, blind yet with an uncanny sense of her surroundings. She was a descendant of the Celestials and depended on the proximity of the Hypersense Stones beneath Sakaimachi to live. She committed suicide for an unknown reason. The Reflector Device was brought by her from her "homeland".


text: Once all jewels are collected, Takuya can enter Triangle Mountain during the correct time. A device there transports him to another world and he loses the Reflector Device. He wakes up confused in a forest and meets a mute blonde pointy-eared girl whose name he deduces as Sayless. The forest is isolated by a cliff beyond which nothing but clouds are visible, and a huge desert. They find the house of a sick knight named Illia, who tells him that the world is Dela Grante; that its inhabitants have pointy ears (like Sayless and Illia); that she is guarding it from monsters arriving from beyond the cliff, known as The Border; that every 400 years a priestess prevents an apocalypse by inhibiting a bodily function to allow "God" within her and being killed in a ritual in a city known as the Capital; that Sayless is an escaped such priestess despite recent earthquakes signifying the current apocalypse; and that Illia has a sister with no faith in Dela Grante's religion. Illia is then fatally injured when protecting Sayless from a monster.


text: Takuya can't cross the desert, but eventually his frustration and homesickness give way to love towards Sayless, and the two begin a happy life in Illia's house. A baby girl, Yu-no, is born to them, and grows within only four years to a teenager-like appearance. One day a dying member of nogards, a species of winged humanoids, arrives and entrusts them with her lizard-form infant, named Kun-kun by Yu-no.


text: Their idyllic life is interrupted as they're invaded by knights from the Capital, and Sayless commits suicide upon capture. Takuya swears revenge on the God Emperor, ruler of Dela Grante residing in the Capital. Leaving Kun-kun behind, Takuya and Yu-no barely cross the desert; however, they are arrested for trespassing a temple and are separated. Takuya ends up working for months in a quarry where enslaved prisoners mine Hypersense Stones for a casket required for the priestess ritual. A machine tower like the one inside Sword Cape uses lightning to kill any slave attempting to escape. Takuya befriends another prisoner, Amanda, who resembles Kanna's mother; she is the leader of a rebel faction believing that the apocalypse and ritual are a lie by the God Emperor to keep the people in control. An earthquake destroys the quarry, leaving as the only survivors Takuya, Amanda, and the now adult Kun-kun who saves them by flying. They head for the Capital, and along the way Kun-kun becomes exhausted from carrying the other two across the desert and is eaten by them, Amanda is saddened upon learning of her sister Illia's death and has sex with Takuya, and they find a Reflector Device at a temple.


text: Once in the Capital, Takuya encounters a new priestess commanding troops and escapes from her into the sewers, which lead to a prison beneath the Emperor's palace. There he meets an imprisoned Ryuuzouji, who reveals that the latest priestess lost her mind as a bodily function to give up, making Takuya realise the current priestess is a brainwashed Yu-no. Takuya frees him in exchange for the information and sneaks into the palace where he cures Yu-no back to normal using Ryuuzouji's advice. Several reveals follow: The God Emperor is actually the Ayumi from the prologue, and was transported alongside Ryuuzouji to Dela Grante by the spacetime distortion; her intentions are good as the ritual is genuine; Dela Grante was constructed 8000 years earlier by a scientifically advanced race as a place to escape an impending apocalypse on Earth; Dela Grante is in an unstable interdimensional orbit around Earth and the ritual is needed every 400 years to avoid a catastrophic collision between the worlds - the computerised mind of ancient head scientist Grantia inhabits a priestess' body to steer Dela Grante, after which the priestess is ejected from the dimension and likely dies; each 400 years the worlds were also so close that some people crossed them, including previous priestess Keiko, explaining the Celestials; the race genetically modified people to have short childhoods and long lifespans but they became dependent on Hypersense Stones; they made other species to survive Dela Grante and discarded failed specimens beyond the Border; later generations couldn't understand the technology and interpreted it religiously; Eriko, who is an interdimensional investigator named Äichli:kkwádroú from yet another world, appears (later explaining smoking was foreign to her world and that she slept on the floor as a remedy for interdimensional travel); Ryuuzouji's body has been possessed the whole time by an entity, which is pursued by Eriko for effectively killing her lover by possessing him and had then arrived at Ryuuzouji's using the interdimensional vehicle. The night before the ritual, Yu-no pleads to have sex with Takuya, who reluctantly complies.


text: The entity attempts to prevent the ritual because it'd survive the annihilation of the worlds and so escape Eriko, but is defeated - after expelling Amanda into another dimension (said to possibly end up on Earth) with a 50 year maximum time difference, and mortally wounding Ayumi. Earth is saved thanks to Yu-no, but Dela Grante inevitably meets its end by colliding on Earth 8000 years in the past, and Yu-no is thrust out of Dela Grante's dimension. With the Reflector Device, and a jewel he gave her, Takuya returns to the moment at Sword Cape where he first saw Yu-no, who was the naked woman in the prologue. The two then begin drifting in a void between dimensions to the beginning of time.


text: Having made the earlier successful adventure games "DESIRE" (1994) and "EVE Burst Error" (1995) at C's Ware, Hiroyuki Kanno and Ryu Umemoto were hired by ELF to create a game with a high budget available. The story Kanno pitched he had developed since his teens, and it was allowed to be fully realized by the budget. As with their earlier projects, Kanno and Umemoto collaborated closely. Each vital plot point was discussed in detail to achieve synergy between story and music, with musical pieces representing the characters' moods and emotions rather than characters or locations. Umemoto, a mathematics prodigy since an early age and a practitioner of Zen Buddhism, applied symbolic elements of his religion to his compositions via mathematical patterns. A new gameplay system called A.D.M.S. (Auto Diverge Mapping System) was made for the game.


text: "YU-NO" was released as an adult game on December 26, 1996, for the NEC PC-98; it was the last MS-DOS-based game developed by ELF. The price at the time was 9800 yen. Both floppy disk and CD-ROM versions were released; the CD-ROM edition contained arrangements of the music but was otherwise identical to the floppy edition.


text: "YU-NO" was released on the Sega Saturn console on December 4, 1997 with a recommended minimum age of 18. The price was 7800 yen, or 9800 yen bundled with a mouse. Several illustrations underneath the CD tray can only be seen after opening the game. A disk containing extra content that was later mailed out with the PC-98 version was integrated into this version. As in the Windows version, some incest references have been removed. Graphics were repainted to use more colors, animation sequences were added, the music was rearranged, character voices were added, two jewels were added (total of 10) and explicit sex scenes were removed.


text: The PC-98 version of the game was ported to Microsoft Windows as part of the "ELF Classics" range and released on December 22, 2000. The graphics and music are equivalent to the PC-98 version but the sexual content was removed.


text: An English-language fan-made translation patch for the Windows version was released in September 2011 by TLWiki. As well as the translation, it provides re-inserted voices from the Sega Saturn version, explicit sex scenes, Ryu Umemoto's original FM score and Sega Saturn CGs. Hardcore Gaming 101 praised the patch for the quality of its translation and called it "one of the finest examples of fan efforts in video gaming".


text: A high-definition video remake of the game was released in March 2017. It was developed by 5pb., which acquired the rights from the now-defunct ELF. It features a remixed soundtrack and new artwork redone in a different style, with Ryo Nagi of "Ar Tonelico" as character designer. The decision for a new art style was made because something easier to depict in animated form was wanted, with the 2019 anime adaptation already in mind. The remake was announced in December 2014 and its release date was delayed several times – first to February 2016, then to the second quarter of 2016, then late 2016 and finally to March 2017.


text: An English localization was released by Spike Chunsoft on October 1, 2019 worldwide for Microsoft Windows, and in North America for Nintendo Switch and PlayStation 4; the game was released in European markets on October 4, 2019. The Switch Day 1 Edition included a side-scrolling shooting game called "8-BIT YU-NO's Great Adventure".


text: In 1997 came out both "Super Soundtrack" and "Original Sound & Voice Collection" soundtrack releases; in 2016 an album titled "Tribute to Ryu Umemoto: Music from YU-NO" featuring remixes by video game composers such as Hiroki Kikuta, Yuji Takenouchi, and Ippo Yamada; and in 2017 alongside the remake a 5-disc collection clocking at 15 hours containing, in addition to the albums from 1997, also recordings of the original PC-98 and remake soundtracks.


text: In 2011, the music of "YU-NO" inspired an eroge tribute music album named "Tree of Knowledge". "RPGFan" said in 2022 that composer Ryu Umemoto's reputation has grown posthumously and praised the 5-disc collection as "must-have for fans of Umemoto, fans of "YU-NO", fans of visual novels, and fans of VGM in general".


text: "YU-NO" holds an average rating of 94 out of 100 on ErogameScape (EGS), making it the second highest-rated visual novel on the site.


text: According to statistics compiled by Digital Media Insider, 45,844 (30,553 CD edition, 15,291 floppy edition) copies were sold by November 30, 1997, excluding ELF's direct mail-order sales. In the 1997 annual ranking in Digital Media Insider, the CD edition was listed in 14th place, with number-one-ranked "SHOCK PRICE Mah-jongg" selling 77,102 copies, and the top-selling adult game "Sadistic King Rance" at number three, selling 72,572 copies.


text: The PC version of "YU-NO" went on to sell over 100,000 copies, as reported in the March 1997 edition of "Comptiq".


text: "YU-NO" won a reader's choice award in Blitz King's "2nd Video Game Awards Grand Prix" in May 1997. The game also was ranked ninth in 's "Game and Heroine of the year 1996", and fifth in "Comptiq"s "1st Video Game Awards Grand Prix" in 1998.


text: The news that the PC-98 edition would be ported to Saturn was reported by several magazines including "", "Dengeki Sega Saturn", and "Famitsu". "Sega Saturn Magazine" included a four-page feature on "YU-NO". The Sega Saturn edition sold 139,509 copies in December 1997, and sold 240,820 copies by February 8, 1998.


text: "Sega Saturn Magazine" scored the game 27 out of 30, with its three reviewers each rating it 9 out of 10. "RPGFan" gave the game a 97% score, including ratings of 100% for story, 100% for control, 85% gameplay, 80% graphics, and 80% sound/music. Reviewer WooJin Lee said the story is "amazing" and praised the A.D.M.S. for adding replay value, concluding that "I feel this game to be THE best Graphical Adventure game ever, which from me (I play tons of these games) is a huge compliment".


text: The Sega Saturn port was voted in 2000 by "Sega Saturn Magazine" readers as the fourth best game on the console, with an average score of 9.4782.


text: The remake sold over 40,000 copies within its first week of release, March 2017, which 5pb celebrated by releasing a "YU-NO"-themed wallpaper. Fall 2019 marked "YU-NO"s first official release in English, via the remake. Its belated arrival outside Japan was greeted with polarised reviews. Some felt that the game was outdated and surpassed by later visual novels, whereas others found it had stood the test of time.


text: "Digitally Downloaded" was captivated by the plot once it moved onto more intellectual topics after what the reviewer saw as a deceptively mundane intro involving a panty shot, proclaiming: "Yu-No is "smart", you come to quickly realise, and then you'll start paying very close attention to every line of dialogue." "RPGFan" was similarly gripped in a new review for the remake. The final route was praised by "Tech-Gaming" as "nothing short of phenomenal"; "Pelit" was less enthusiastic about the route, arguing that despite the surprises the tension was deflated by the lack of the difficult nonlinear gameplay from earlier. While some were also intrigued by the plot, they were put off by the eroge aspects. "RPG Site" criticised Ayumi's route as the game's weakest, dependent on misunderstandings for cheap drama.


text: Many took issue with the game's sexual and ecchi content. "Nintendo Life" felt that the game's "dating-sim elements" and "grandiose narrative" clashed, leading to an "identity crisis". "RPG Site" counted three instances of incest and called two of them "unnecessary and gross". "Digitally Downloaded" held the opinion that there were both justified and unjustified cases of sexual "fanservice", saying they "are on the juvenile side of things just often enough that certain elements of the community will dismiss the game on that basis" but that "even in the fan service it gets things right far, far more often than it misfires." "Pelit"s reviewer conversely had little problem and outright refused to hand out a moral judgement, suggesting that gaming is rather based on rejection of morality in the first place. He concluded that the game has a limited audience of those intrigued by morally grey, erotic weird games and an anime style, and the rest wouldn't last the first five minutes; that encountering the school nurse clad in tight latex was a casual filter.


text: Opinions on the characters were split. "RPG Site", "Nintendo Life" and "Nintendo World Report" couldn't tolerate main character Takuya and his lecherousness. "RPG Site" compared him unfavourably to "Chaos;Child"s Takuru Miyashiro, whose flaws he thought were better taken advantage of thematically in the respective narrative, and found the other characters weak as well. "Nintendo Life" asserted that the characters had become cliché and bland by today's standards. Others saw more depth in the characters. "Digitally Downloaded" defended Takuya's fixation with females as "appropriate characterisation for building the protagonist up as something of a mix of teenage hormones and delinquency in coming from a broken home". "RPGFan" enjoyed exploring the webs of interpersonal relationships, saying: "While characters fall into relatable archetypes, they are complex, compelling, and not always what they seem." "Tech-Gaming" said the nuances of real-life conversations were captured in Takuya's ability to read subtle cues and body language and respond accordingly, causing development over time: "Like an actual person, he's influenced by the people and actions around him, which are mirrored by Takuya, almost imperceptibly."


text: A.D.M.S. with its branching timelines was praised as genius by "Nintendo Life" and "RPG Site", with "Nintendo World Report" calling it "still an impressive gameplay system two decades after its creation". "Pelit" embraced the challenge brought by the gameplay and described it as not only as nostalgically cruel for its item management but also immersive, "as if it was the player themself who was learning the logic of time-jumping and not only Takuya". "RPGFan" was grateful for a hint system introduced in the remake remedying the need of "wild goose chases" to find the next trigger to advance the plot. "Digitally Downloaded" found the requirement of repeatedly checking hotspots in a scene to advance an unnecessary chore. Other than the cursor at all times locking onto interactable areas and the tedium of skipping text in familiar parts, "RPG Site" had little to complain about the gameplay.


text: The English translation received complaints of stiltedness and awkwardness from "RPG Site" and "RPGFan", the former at times being baffled by incomprehensible passages. "RPGFan" noticed that concepts were localised inconsistently throughout, such as whether yen or dollars were used as currency.


text: The remake's artwork had in "Nintendo Life"s opinion a "standard, generic low-budget anime look" and less atmosphere compared to the original PC-98 designs. However, "Digitally Downloaded" called the visuals "gorgeous" and admired how "every scene, character, and environment drips with carefully constructed atmosphere", especially in a lengthy 30-hour game requiring a lot of art and design. Both "Digitally Downloaded" and "RPG Site" wished there was an option for the original art.


text: At "Hardcore Gaming 101", Audun Sorlie wrote that "YU-NO" helped revolutionize the visual novel genre, particularly with the A.D.M.S., which was touted as "revolutionary" at the time. At "Gamasutra", Sorlie wrote that audiences soon began demanding large-scope plotlines and musical scores of similar quality and ambition to that of "YU-NO"'s, and that companies responded by hiring talent: "The genre became an all-new arena for young artists and musicians once again, with companies willing to take chances on fresh blood; the market thrived with the excitement and the risks that were being taken, and became a hotbed of creativity". The branching timeline system was influential, opening "the door for visual novels to become more elaborate and have a greater range of narrative arcs, without requiring the player to replay the game over and over again." It also featured the time loop concept, and an isekai in its final story arc, which has a use of what later became a common anime trope by the 2010s. According to "Nintendo Life", "the modern visual novel genre would simply not exist without" "YU-NO".


text: According to , the influence of "YU-NO" goes beyond visual novels and extends to modern otaku, manga and anime works. The mangaka Tamiki Wakaki, for example, has cited "YU-NO" as an influence on the manga and anime series, "The World God Only Knows". Other visual novel and manga authors who cited "YU-NO" as an influence include Romeo Tanaka, Poyoyon Rock, Key founder Jun Maeda (known for titles such as "Kanon", "Clannad" and "Angel Beats"), Type-Moon's Hikaru Sakurai, "White Album 2" and "Saekano" author Fumiaki Maruto, and "To Heart" author Toru Minazuki.


text: According to Anime News Network, "YU-NO" is "considered one of the most beloved narrative games in Japan, and its system of parallel storylines had a profound influence on storytelling in visual novels in the years since its original release." They said it "was incredibly popular for its time and likely inspired a lot of media after its release" and they noted its premise is "adjacent to "Steins;Gate"." According to RPG Site and DualShockers, "YU-NO" influenced later visual novels such as "Fate/stay night" and "Steins;Gate". According to "Nintendo World Report", visual novels such as "Ace Attorney", "Fate/stay night" and "Steins;Gate" owe their success to "YU-NO".


text: Pink Pineapple produced and released a four-episode hentai anime original video animation series during 1998–1999. The anime had multiple changes from the original game such as cutting multiple characters and adding characters from the A.D.M.S. section into the Epilogue.


text: A new, 26-episode anime adaptation began airing on April 2, 2019 for half a year. Announced in 2016, it was produced by Feel in collaboration with MAGES and Genco and was broadcast on AT-X, Tokyo MX, ABC, and BS Fuji, with Crunchyroll and Funimation streaming outside Japan with an additional English dub. The anime is directed by Tetsuo Hirakawa, and the characters are designed by Mai Otsuka. Kazuya Tanaka is the sound director, and Keishi Yonao and Ryu Takami were assigned to compose the series' music. Asaka performed the series' opening theme song , while Konomi Suzuki performed the series' ending theme song Suzuki performed the series' second opening theme song "MOTHER", while Asaka performed the series' second ending theme song .


text: Hirakawa said the anime would include all characters and routes from the original game. Unlike the game's first-person perspective from protagonist Takuya's point of view, the anime was declared to depict the relationships of the girls surrounding Takuya. Hirakawa also said the anime would "outdo the game in dirty jokes", that Mio would "be even more tsundere", and that Kanna would "be even more mysterious".


text: A manga adaptation by Mario Kaneda was published in Enix's G Fantasy magazine from 1997 to 1998. A manga adaptation by Sōji Ishida ran in Enterbrain's Comic Clear magazine from March 14, 2017 to March 15, 2018.


title: Logistic map

text: The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst.


title: Logistic map

text: where is a number between zero and one, that represents the ratio of existing population to the maximum possible population.


title: Logistic map

text: The usual values of interest for the parameter are those in the interval , so that remains bounded on . The case of the logistic map is a nonlinear transformation of both the bit-shift map and the case of the tent map. If this leads to negative population sizes. (This problem does not appear in the older Ricker model, which also exhibits chaotic dynamics.) One can also consider values of in the interval , so that remains bounded on .


title: Logistic map

text: The image below shows the amplitude and frequency content of some logistic map iterates for parameter values ranging from 2 to 4.


title: Logistic map

text: For any value of there is at most one stable cycle. If a stable cycle exists, it is globally stable, attracting almost all points. Some values of with a stable cycle of some period have infinitely many unstable cycles of various periods.


title: Logistic map

text: The bifurcation diagram at right summarizes this. The horizontal axis shows the possible values of the parameter while the vertical axis shows the set of values of visited asymptotically from almost all initial conditions by the iterates of the logistic equation with that value.


title: Logistic map

text: The bifurcation diagram is a self-similar: if we zoom in on the above-mentioned value and focus on one arm of the three, the situation nearby looks like a shrunk and slightly distorted version of the whole diagram. The same is true for all other non-chaotic points. This is an example of the deep and ubiquitous connection between chaos and fractals.


title: Logistic map

text: The relative simplicity of the logistic map makes it a widely used point of entry into a consideration of the concept of chaos. A rough description of chaos is that chaotic systems exhibit a great sensitivity to initial conditions—a property of the logistic map for most values of between about 3.57 and 4 (as noted above). A common source of such sensitivity to initial conditions is that the map represents a repeated folding and stretching of the space on which it is defined. In the case of the logistic map, the quadratic difference equation describing it may be thought of as a stretching-and-folding operation on the interval .


title: Logistic map

text: The following figure illustrates the stretching and folding over a sequence of iterates of the map. Figure (a), left, shows a two-dimensional Poincaré plot of the logistic map's state space for , and clearly shows the quadratic curve of the difference equation (). However, we can embed the same sequence in a three-dimensional state space, in order to investigate the deeper structure of the map. Figure (b), right, demonstrates this, showing how initially nearby points begin to diverge, particularly in those regions of corresponding to the steeper sections of the plot.


title: Logistic map

text: This stretching-and-folding does not just produce a gradual divergence of the sequences of iterates, but an exponential divergence (see Lyapunov exponents), evidenced also by the complexity and unpredictability of the chaotic logistic map. In fact, exponential divergence of sequences of iterates explains the connection between chaos and unpredictability: a small error in the supposed initial state of the system will tend to correspond to a large error later in its evolution. Hence, predictions about future states become progressively (indeed, exponentially) worse when there are even very small errors in our knowledge of the initial state. This quality of unpredictability and apparent randomness led the logistic map equation to be used as a pseudo-random number generator in early computers.


title: Logistic map

text: Since the map is confined to an interval on the real number line, its dimension is less than or equal to unity. Numerical estimates yield a correlation dimension of (Grassberger, 1983), a Hausdorff dimension of about 0.538 (Grassberger 1981), and an information dimension of approximately 0.5170976 (Grassberger 1983) for (onset of chaos). Note: It can be shown that the correlation dimension is certainly between 0.4926 and 0.5024.


title: Logistic map

text: It is often possible, however, to make precise and accurate statements about the "likelihood" of a future state in a chaotic system. If a (possibly chaotic) dynamical system has an attractor, then there exists a probability measure that gives the long-run proportion of time spent by the system in the various regions of the attractor. In the case of the logistic map with parameter and an initial state in , the attractor is also the interval and the probability measure corresponds to the beta distribution with parameters and . Specifically, the invariant measure is


title: Logistic map

text: Unpredictability is not randomness, but in some circumstances looks very much like it. Hence, and fortunately, even if we know very little about the initial state of the logistic map (or some other chaotic system), we can still say something about the distribution of states arbitrarily far into the future, and use this knowledge to inform decisions based on the state of the system.


title: Logistic map

text: Although exact solutions to the recurrence relation are only available in a small number of cases, a closed-form upper bound on the logistic map is known when . There are two aspects of the behavior of the logistic map that should be captured by an upper bound in this regime: the asymptotic geometric decay with constant , and the fast initial decay when is close to 1, driven by the term in the recurrence relation. The following bound captures both of these effects:


title: Logistic map

text: The special case of can in fact be solved exactly, as can the case with ; however, the general case can only be predicted statistically.


title: Logistic map

text: For rational , after a finite number of iterations maps into a periodic sequence. But almost all are irrational, and, for irrational , never repeats itself – it is non-periodic. This solution equation clearly demonstrates the two key features of chaos – stretching and folding: the factor shows the exponential growth of stretching, which results in sensitive dependence on initial conditions, while the squared sine function keeps folded within the range .


title: Logistic map

text: with modulus equal to 1. Just as the squared sine function in the trigonometric solution leads to neither shrinkage nor expansion of the set of points visited, in the latter solution this effect is accomplished by the unit modulus of .


title: Logistic map

text: for . Since for any value of other than the unstable fixed point 0, the term goes to 0 as goes to infinity, so goes to the stable fixed point .


title: Logistic map

text: For the case, from almost all initial conditions the iterate sequence is chaotic. Nevertheless, there exist an infinite number of initial conditions that lead to cycles, and indeed there exist cycles of length for "all" integers . We can exploit the relationship of the logistic map to the dyadic transformation (also known as the "bit-shift map") to find cycles of any length. If follows the logistic map and follows the "dyadic transformation"


title: Logistic map

text: The reason that the dyadic transformation is also called the bit-shift map is that when is written in binary notation, the map moves the binary point one place to the right (and if the bit to the left of the binary point has become a "1", this "1" is changed to a "0"). A cycle of length 3, for example, occurs if an iterate has a 3-bit repeating sequence in its binary expansion (which is not also a one-bit repeating sequence): 001, 010, 100, 110, 101, or 011. The iterate 001001001... maps into 010010010..., which maps into 100100100..., which in turn maps into the original 001001001...; so this is a 3-cycle of the bit shift map. And the other three binary-expansion repeating sequences give the 3-cycle 110110110... → 101101101... → 011011011... → 110110110... Either of these 3-cycles can be converted to fraction form: for example, the first-given 3-cycle can be written as → → → . Using the above translation from the bit-shift map to the formula_11 logistic map gives the corresponding logistic cycle 0.611260467... → 0.950484434... → 0.188255099... → 0.611260467... We could similarly translate the other bit-shift 3-cycle into its corresponding logistic cycle. Likewise, cycles of any length can be found in the bit-shift map and then translated into the corresponding logistic cycles.


title: Logistic map

text: However, since almost all numbers in are irrational, almost all initial conditions of the bit-shift map lead to the non-periodicity of chaos. This is one way to see that the logistic map is chaotic for almost all initial conditions.


title: Logistic map

text: The number of cycles of (minimal) length for the logistic map with (tent map with ) is a known integer sequence : 2, 1, 2, 3, 6, 9, 18, 30, 56, 99, 186, 335, 630, 1161... This tells us that the logistic map with has 2 fixed points, 1 cycle of length 2, 2 cycles of length 3 and so on. This sequence takes a particularly simple form for prime : . For example: 2 ⋅  = 630 is the number of cycles of length 13. Since this case of the logistic map is chaotic for almost all initial conditions, all of these finite-length cycles are unstable.


title: Logistic map

text: Universality of one-dimensional maps with parabolic maxima and Feigenbaum constants formula_12, formula_13 is well visible with map proposed as a toy


title: Logistic map

text: where formula_15 stands for electric field amplitude, formula_16 is laser gain as bifurcation parameter.


title: Logistic map

text: The gradual increase of formula_16 at interval formula_18 changes dynamics from regular to chaotic one with qualitatively the same bifurcation diagram as those for logistic map.


title: Golden Globe Award for Best Actor – Motion Picture Drama

text: The Golden Globe Award for Best Actor in a Motion Picture – Drama is a Golden Globe Award that was first awarded by the Hollywood Foreign Press Association as a separate category in 1951. Previously, there was a single award for "Best Actor in a Motion Picture" but the splitting allowed for recognition of it and the Best Actor – Musical or Comedy.


text: The formal title has varied since its inception. In 2005, it was officially called: "Best Performance by an Actor in a Motion Picture – Drama". , the wording is "Best Actor in a Motion Picture – Drama".


title: Dunhill (cigarette)

text: Dunhill is a Westminster, London-based luxurious cigarette owned and manufactured by Dunhill and British American Tobacco. The brand name commemorates the English tobacconist, entrepreneur and inventor Alfred Dunhill. In the United Kingdom, Dunhill is registered and manufactured in Westminster, City of Westminster, London.


title: Dunhill (cigarette)

text: Dunhill was founded in London on 10 March 1907 when tobacconist and inventor Alfred Dunhill opened a small tobacconist's shop on Duke Street in the St James's area. He offered tobacco blends tailored for the individual customer. Dunhill was introduced in 1908 and was, less than glamorously, called the Absorbal. It was designed to counter any perceived health risk and had "a world first" - a cotton wool filter tip. Its slogan was the ""Hygienic Cigarette"". Dunhill cigarettes had a royal warrant from 1927 until 1995.


title: Dunhill (cigarette)

text: In 1939 the brand was introduced in the United States by Philip Morris USA who leased the marketing rights for the U.S. and in 1962, "Dunhill International" was introduced.


title: Dunhill (cigarette)

text: Dunhill cigarettes are usually priced above the average for cigarettes in the region where they are sold due to the use of higher-quality tobacco.


title: Dunhill (cigarette)

text: "Dunhill" (minus the ""International"") is a more expensive version produced by BAT, and are sold in European (including Russia), Asia-Pacific, South African and Canadian markets.


title: Dunhill (cigarette)

text: Dunhill also markets a line of cigarillos in Malaysia. It is made of 100% tobacco inside out, whereby even the cigarette wrapper is made from tobacco using homogenized tobacco leaves.


title: Dunhill (cigarette)

text: In 2012, it was reported that British American Tobacco was breaking anti-tobacco rules in Nigeria and South Africa by illegally advertising their Dunhill brand in both countries. It was reported that in South Africa, a 14 year old girl was giving away the cigarettes, but also that BAT engages in industrial espionage, intensive cross-border smuggling, competitor tyranny, and infiltrating governments. Despite South Africa having one of the toughest anti-tobacco laws in Africa, the company failed to comply with the law, pushing on in both government fronts and covert advertising and promotions. In Nigeria meanwhile, BAT controls 84% of the cigarette market. In 2010, while markets in Turkey, Iran and South Africa declined, BAT's profit from the African and Middle East regions grew by £134 million to £858 million, driven largely by its Nigerian market.


title: Dunhill (cigarette)

text: The cover art for "The 'Sweetest Girl'", a single by British pop band Scritti Politti, pays homage to the packaging of Dunhill.


title: Grand Prairie, Texas

text: Grand Prairie is a city in Dallas, Tarrant, and Ellis counties of Texas, in the United States. It is part of the Mid-Cities region in the Dallas–Fort Worth metroplex. It had a population of 175,396 according to the 2010 census, making it the fifteenth most populous city in the state. Remaining the 15th-most populous city in Texas, the 2020 census reported a population of 196,100.


title: Grand Prairie, Texas

text: The city of Grand Prairie was first established as Dechman by Alexander McRae Dechman in 1863. He based the name of the town on Big Prairie, Ohio. Prior to then, he resided in Young County near Fort Belknap. The 1860 U.S. Federal Census—Slave Schedules shows an A McR Dechman as having 4 slaves, ages 50, 25, 37 and 10. Dechman learned that he could trade his oxen and wagons for land in Dallas County. In 1863, Dechman bought of land on the eastern side of the Trinity River and of timber land on the west side of the river for a broken-down wagon, oxen team and US$200 in Confederate money. He tried to establish a home on the property, but ran into difficulties, so he returned to his family in Birdville before joining in the Civil War. In 1867 he filed a town plat with Dallas County, consisting of .


title: Grand Prairie, Texas

text: After the war, he returned to Birdville for two years before selling that farm in 1867 and moving to Houston, where yellow fever broke out, causing the family to settle in Bryan. In 1876, Dechman traded half his "prairie" property to the T&P Railroad to ensure the railroad came through the town. The railroad named the depot "Dechman", prompting its namesake to relocate his home from Bryan to Dechman. His son Alexander had been living in Dechman and operating a trading post and farm. The first church in the area was the Good Hope Cumberland Sabbath School, established in 1870 by Rev. Andrew Hayter. The church was later renamed West Fork United Presbyterian Church and remains an active church.


title: Grand Prairie, Texas

text: The first U.S. post office opened in 1877 under the name "Deckman" rather than "Dechman", because the U.S. Postal Service couldn't read the writing on the form completed to open the post office. Later that same year, after the Postal Service had adopted the "Deckman" name, confusion resulted from the T&P Railroad designation "Grand Prairie". This name was based on maps drawn from around 1850 through 1858 that labeled the area between Dallas and Fort Worth "the grand prairie of Texas". In order to alleviate the confusion, the Postal Service named the post office "Grand Prairie".


title: Grand Prairie, Texas

text: The town of Grand Prairie was eventually incorporated as a city in 1909. During World War I and since, Grand Prairie has had a long history with the defense and aviation industry. While the present-day Vought plant on Jefferson Avenue is part of a small strip within the Dallas city limits, it was originally in Grand Prairie. During World War II the North American Aviation Plant B produced the Consolidated B-24 Liberator and the P-51C and K Mustang variants. After the war, Vought Aircraft took over the plant. This later became Ling Temco Vought (LTV) and then eventually returned to the Vought moniker. The plant was the production site for the F-8 Crusader and the A-7 Corsair II aircraft of the 1950–1989 time period. The LTV Missile and Space division produced missiles such as the Scout and MLRS. This division was eventually sold to Lockheed Martin, which continues to operate in Grand Prairie. Grand Prairie was also the North American headquarters for Aérospatiale Helicopter. This company eventually became Airbus Helicopters, Inc., the U.S. subsidiary of Airbus Helicopters.


title: Grand Prairie, Texas

text: In 1953, the mayor and city council of Grand Prairie attempted to annex nearly of then-unincorporated and largely undeveloped land in southern Dallas and Tarrant counties. Vehement debate ensued, and the legal pressure from cities like Arlington, Duncanville and Irving wound up overturning part of the annexation attempt.


title: Grand Prairie, Texas

text: Grand Prairie is located along the border between Tarrant and Dallas counties, with a small portion extending south into Ellis County. The city is bordered by Dallas to the east, Cedar Hill and Midlothian to the southeast, Mansfield to the southwest, Arlington to the west, Fort Worth to the northwest, and Irving to the north.


title: Grand Prairie, Texas

text: According to the United States Census Bureau, the city has a total area of , of which is land and , or 11.08%, is water.


title: Grand Prairie, Texas

text: Grand Prairie has a long history of flooding from Johnson Creek. In the 1980s, a major Army Corps of Engineers project was begun to straighten the channel, which has reduced the damage of flooding.


title: Grand Prairie, Texas

text: As of the 2020 United States census, there were 196,100 people, 62,679 households, and 46,391 families residing in the city.


title: Grand Prairie, Texas

text: According to the city's 2007–2008 Comprehensive Annual Financial Report, the city's various funds had $275.5 million in revenues, $236.4 million in expenditures, $1,003.2 million in total assets, $424.9 million in total liabilities, and $305.9 million in cash and investments.


title: Grand Prairie, Texas

text: The Parkland Health & Hospital System (Dallas County Hospital District) operates the E. Carlyle Smith, Jr. Health Center in Grand Prairie.


title: Grand Prairie, Texas

text: The city of Grand Prairie is a voluntary member of the North Central Texas Council of Governments association, the purpose of which is to coordinate individual and collective local governments and facilitate regional solutions, eliminate unnecessary duplication, and enable joint decisions.


title: Grand Prairie, Texas

text: The Bureau of Prisons (BOP), of the U.S. Department of Justice runs the Grand Prairie Office Complex on the grounds of the Grand Prairie Armed Forces Reserve Complex. Within the complex the BOP operates the Designation and Sentence Computation Center (DSCC), which calculates federal sentences, keeps track of the statutory "good time" accumulated by inmates and lump sum extra "good time" awards, and detainers. The BOP South Central Office is also on the armed forces complex grounds.


title: Grand Prairie, Texas

text: According to the city's 2018 Comprehensive Annual Financial Report, the top employers in the city were:


title: Grand Prairie, Texas

text: Airbus Helicopters, Inc., the U.S. subsidiary of Airbus Helicopters, has its headquarters in Grand Prairie.


title: Grand Prairie, Texas

text: In 1978 American Airlines announced that it would move its headquarters from New York City to the Dallas/Fort Worth area. The airline moved its headquarters into two leased office buildings in Grand Prairie. The airline finished moving into its Fort Worth headquarters facility on January 17, 1983, when the airline left its Grand Prairie facility.


title: Grand Prairie, Texas

text: Most of Grand Prairie's K–12 student population attends schools in the Grand Prairie Independent School District, which serves areas of Grand Prairie in Dallas County. The Mansfield Independent School District serves areas of Grand Prairie in Tarrant County and operates six elementary schools within the Grand Prairie city limits. Other portions of Grand Prairie reside within the Arlington, Cedar Hill, Irving, Mansfield, and Midlothian school districts.


title: Grand Prairie, Texas

text: In Texas, school district boundaries do not follow city and county boundaries because all aspects of the school district government apparatus, including school district boundaries, are separated from the city and county government entirely, with the exception of the Stafford Municipal School District in the Houston area.


title: Grand Prairie, Texas

text: The Arlington ISD has the second highest portion of Grand Prairie's K–12 student population. Six Arlington ISD elementary schools are within the city limits of Grand Prairie. Grand Prairie residents in the Arlington ISD are located generally west of the Dallas-Tarrant County boundary and north of the intersection of Camp Wisdom and Lake Ridge in southwest Grand Prairie. One of the Arlington high schools, James Bowie High, has more Grand Prairie residents than Arlington residents that are students at the school.


title: Grand Prairie, Texas

text: Grand Prairie student/residents in the Arlington ISD attend Bowie, Sam Houston, or Lamar High School in the Arlington ISD and their feeder elementary schools and junior high schools.


title: Grand Prairie, Texas

text: The Mansfield ISD contains the third highest portion of the Grand Prairie's K–12 student population. Grand Prairie residents in the Mansfield ISD are located generally south of the intersection of Camp Wisdom and Lake Ridge, and west of Joe Pool Lake to the Tarrant and Ellis County line in southwest Grand Prairie. Three Mansfield ISD schools, Anna May Daulton Elementary; Louise Cabaniss Elementary; and Cora Spencer Elementary, are currently open within the city limits of Grand Prairie. The Mansfield ISD is the fastest growing ISD in Tarrant County, and the population growth in far southwest Grand Prairie is a major factor in the Mansfield ISD's subsequent growth.


title: Grand Prairie, Texas

text: Grand Prairie students/residents in the Mansfield ISD attend Mansfield Timberview High School, Lake Ridge High School or Mansfield High School in the Mansfield ISD or their feeder elementaries and middle schools. Timberview High School is located on State Highway 360 less than from the Grand Prairie city line.


title: Grand Prairie, Texas

text: Dallas County residents are zoned to Dallas College (formerly Dallas County Community College District or DCCCD). Tarrant County residents are zoned to Tarrant County Junior College. Ellis County residents are zoned to Navarro College.


title: Grand Prairie, Texas

text: Interstate highways 20 and 30 run east–west through the northern and southern parts of the city. Texas State Highways Spur 303 (named Pioneer Parkway) and 180 (Main Street) also run east–west in the northern and central portions of the city.


title: Grand Prairie, Texas

text: SH 360 runs for almost three miles in the northwestern portion of city; most of the highway runs just west of the city limits in Arlington.


title: Grand Prairie, Texas

text: SH 161, named the President George Bush Turnpike, runs north–south through western Grand Prairie. The main lanes were opened in late 2012 with frontage roads open since 2010. Portions of the highway located north of SH 180 are depressed while the portion south of SH 180 runs at-grade then becomes elevated. Frontage roads remain at-grade throughout. The frontage road intersection at Main Street will open sometime in 2013.


title: Grand Prairie, Texas

text: Belt Line Road is a major north–south thoroughfare in the city. The section of the road south of Main Street is dual-labelled as FM 1382, which travels south, past I-20 and continues south to Cedar Hill. The section of the road north of Main Street keeps its name, continuing north into Irving.


title: Grand Prairie, Texas

text: The city declined membership in 1984. In April 2022, Grand Prairie launched "Via Grand Prairie", an "on-demand, shared public transportation" which connects to DART's West Irving station.


title: Grand Prairie, Texas

text: In the era of private operation of passenger trains prior to the onset of the Amtrak era in 1971, Texas and Pacific Railway trains such as the "Texas Eagle" and the "Louisiana Eagle" made stops in Grand Prairie, on trips between Fort Worth and Dallas. Amtrak's "Texas Eagle" (Chicago-San Antonio) makes stops at Dallas Union Station 12 miles to the east.


title: Saamy Square

text: Saamy 2, Also known as Saamy Square,Cringe Square, is a 2018 Indian Tamil-language action film written and directed by Hari and produced by Shibu Thameens. It stars Vikram in a double role as a father and son, with Keerthy Suresh and Aishwarya Rajesh as the female leads alongside Prabhu, Bobby Simha, and Soori in supporting roles.


title: Saamy Square

text: The film is a sequel to the 2003 film "Saamy". The film was released theatrically on 21 September 2018.


title: Saamy Square

text: Deputy commissioner Aarusaamy (Vikram), who had been transferred out of Tirunelveli after finishing off evil politician Perumal Pichai, leads a happy life with his now-pregnant wife Bhuvana (Aishwarya Rajesh) in Palani, who intends to pursue IAS. However, in Tirunelveli, Perumal Pichai's men, who were discussing what happened to him, assume that he might be in Colombo with Perumal Pichai's wife (Sudha Chandran) and three sons: Mahendra Pichai (O. A. K. Sundar), the eldest; Devendra Pichai (John Vijay), the second-eldest; and the Raavana Pichai (Bobby Simha), the youngest. Among them, Raavana is more dangerous and ruthless than Devendra and Mahendra. 28 years pass. Aarusaamy's son Ramasaamy (Vikram) lives in New Delhi and works under the Union Home Minister, Viswanathan (Prabhu). The Minister's daughter, Diya (Keerthy Suresh), who has returned from London after completing her studies and who constantly disagrees with him.


title: Saamy Square

text: Later, when Raavana asks Viswanathan for the pending commission amount to be paid for transferring the party fund secretly, he simply replies to ask the party directly and not him. Irritated, Raavana kidnaps Diya for immediate settlement of payment. Ram rescues her from Raavana's goons and drops her home. She is impressed by his diplomatic nature and falls in love with him. Soon after, Ram accidentally happens to seize a van containing black money being transferred by Raavana on a commission basis. He hands the money over to the President of India without revealing his identity, which once again frustrates Raavana. Diya constantly proposes to Ram, which he rejects initially but gives in later.


title: Saamy Square

text: Ram succeeds in the UPSC exam and leaves for Mussoorie for one-year training. After his return, his maternal grandparents are shell shocked to see that he has opted for IPS and that he has been posted as probationary Assistant commissioner in Tirunelveli. When Ram asks the reason for their reaction, his grandfather tells the truth that, in fact, his father, Aarusaamy, has been a Deputy commissioner in Tirunelveli. Ram's maternal grandfather begins to explain what happened 28 years ago. When Saamy and Bhuvana were on their way to Tirunelveli, they were hacked to death by the Pichai brothers to avenge their father's death. Before dying, Saamy manages to open his dead wife's uterus and prematurely deliver his child (Ram). Bhuvana's parents take Ram and escape to Delhi, while the rest of their family is killed by a truck accident planned by Raavana.


title: Saamy Square

text: Agitated by hearing his tragic past, Ram decides to go to Tirunelveli and get justice for his parents' death. Ram's maternal grandparents accept his decision, and he leaves for Tirunelveli and decides to take on the Pichai brothers. He initially warns Raavana and vows to bring the Pichai brothers before the law for killing his parents. Ram later razes Perumal's statue, which had been illegally placed at an intersection by Raavana and caused a lot of traffic problems. A cat-and-mouse game ensues between Ram and Raavana, with both of them trying to get rid of each other. Per the president's orders, Sammy is transferred to Tirunelveli and by this, Raavan gets surprised as they were not able to make a transfer elsewhere. Meanwhile, Viswanathan initially disapproves of Ram and Diya's love, but he later accepts it.


title: Saamy Square

text: Ram kills Devendra and Mahendra after an accident caused by them in Devendra's cracker factory to prevent Ram from seizing illegal extortion money of Raavana, which kills many innocent workers, as well as pregnant women.


title: Saamy Square

text: Raavana's goons start to kill the people of Tirunelveli in revenge. Viswanathan makes a decision to resign from politics for embarrassment faced. In the mean while, Raavana's henchmen orchestrate a train accident which kills Viswanathan.


title: Saamy Square

text: Ram finds out that Raavana is planning to go to Pakistan via Gujarat and Rajasthan, he tracks him down. After a tiresome fight with desert bandits and Raavana, Ram subdues Raavana but decides to leave him to his fate in the middle of the Thar Desert with no man, town, village, or water source for several hundreds of kilometres.


title: Saamy Square

text: As the credits roll, Ram lies to the media that Raavana had left for Sri Lanka due to fear of being killed. There is a record of Raavana, going to Sri Lanka, but there is no record of coming back to India. Whereas, Raavana dies after 17 days in the desert. Soon, Ram and Diya marry. The movie ends with the message, "Saamy's adventure will continue".


title: Saamy Square

text: In August 2016, during the audio launch of "Iru Mugan", director Hari made an official announcement that he would unite with Vikram, also echoed by the latter, for a sequel to "Saamy" after 13 years being bankrolled by Shibu Thameens. The principal photography was expected to commence in late 2016 with Harris Jayaraj as music composer. During December 2016, Shibu Thameens confirmed that the plan for sequel was still on, putting an end to the rumours of the project being shelved, as director Hari and his team were involved in script development and would tentatively commence the principal photography in April 2017. In May 2017, it was officially announced that Devi Sri Prasad would be the composer, collaborating again with Vikram for the second time after "Kanthasamy" and Hari for the fifth time after "Aaru", "Venghai", "Singam" and "Singam 2". In August 2017, it was reported that lyricist Viveka had joined the composer and director for a music composition session at Puducherry. Kanal Kannan and Silva were tasked with action choreography. Priyan, Hari's regular cinematographer, was selected as well, but later Venkatesh Anguraj became the cinematographer after Priyan died due to a heart attack in November 2017. The art direction was done by P. Shanmugam and P.V. Balaji, replacing K. Kadhir, who had collaborated with Hari in his previous films.


title: Saamy Square

text: Apart from Vikram reprising his role, Keerthy Suresh was selected as the female lead. Prabhu and comedian Soori were added to cast along with Bobby Simha. Trisha was originally going to reprise her role as Bhuvana from the first film, but opted out citing "creative differences"; she was replaced by Aishwarya Rajesh.


title: Saamy Square

text: Despite the commencement of pre-production, the shooting was supposed to be commenced during June or July 2017 as quoted by the film producer. Various sources towards reported that the shoot would start towards the end of September 2017. Finally, the principal photography commenced in Chennai from 30 September 2017 onwards. The director also revealed that the film would be shot in Delhi, Mussoorie and Nepal after shooting considerable portions in Chennai. In early October, the film's new title was revealed to be "Saamy Square". Most of the scenes were shot at various locations within the city of Trivandrum and also in Karaikudi by setting the name of Thirunelveli.


title: Saamy Square

text: "Saamy 2" received highly negative reviews from critics, by criticizing the outdated story, humours, screenplay, music and lack of standard comparing to its first part. However, the film's cast performance received praise. The film was flagged as a "box-office bomb". The satellite rights of the film were sold to STAR Vijay. The film was later dubbed and released in Hindi by Pen Movies directly on TV channel Zee Cinema on 10 November 2019.


title: Saamy Square

text: Indiaglitz called the movie "A Speedy journeys to Nowhere" in their review. They added, "Go for this ride if you are a fan of Vikram and are immune to Deja Vu".


title: Saamy Square

text: The music was composed by Devi Sri Prasad, who replaces the predecessor's music composer Harris Jayaraj. This film marks the Tamil comeback of music composer Devi Sri Prasad after a hiatus of three years, whose previous Tamil film was "Puli" (2015).


title: Saamy Square

text: Sony Music acquired the rights of the soundtrack for the film. All lyrics were written by Viveka, except one song, which was penned by the composer himself.


title: Saamy Square

text: The first single, "Adhiroobaney," was released on 10 July 2018, with lyrics being penned by Viveka and sung by M. M. Manasi. The second single, "Molaga Podiye," soon followed and released on 18 July 2018. The full soundtrack album of the Tamil version was released on 23 July 2018.


title: Anglo-Scottish border

text: The Anglo-Scottish border () is a border separating Scotland and England which runs for 96 miles (154 km) between Marshall Meadows Bay on the east coast and the Solway Firth in the west. The surrounding area is sometimes referred to as "the Borderlands".


title: Anglo-Scottish border

text: The Firth of Forth was the border between the Picto-Gaelic Kingdom of Alba and the Anglian Kingdom of Northumbria in the early 10th century. It became the first Anglo-Scottish border with the annexation of Northumbria by Anglo-Saxon England in the mid-10th century. In 973, Kenneth, King of Scots attended the English king, Edgar the Peaceful, at his council in Chester. After Kenneth had reportedly done homage, Edgar rewarded Kenneth by granting him Lothian. Despite this transaction, the control of Lothian was not finally settled and the region was taken by the Scots at the Battle of Carham in 1018 and the River Tweed became the "de facto" Anglo-Scottish border. The Solway–Tweed line was legally established in 1237 by the Treaty of York between England and Scotland. It remains the border today, with the exception of the Debatable Lands, north of Carlisle, and a small area around Berwick-upon-Tweed, which was taken by England in 1482. Berwick was not fully annexed into England until 1746, by the Wales and Berwick Act 1746.


title: Anglo-Scottish border

text: For centuries until the Union of the Crowns the region on either side of the boundary was a lawless territory suffering from the repeated raids in each direction of the Border Reivers. Following the Treaty of Union 1706, ratified by the Acts of Union 1707, which united Scotland with England and Wales to form the Kingdom of Great Britain, the Border forms the boundary of the two legal systems as the treaty between Scotland and England guaranteed the continued separation of English law and Scots law. The age of marriage under Scots law is 16, while it is 18 under English law. The border settlements of Gretna Green to the west, and Coldstream and Lamberton to the east, were convenient for elopers from England who wanted to marry under Scottish laws, and marry without publicity.


title: Anglo-Scottish border

text: The marine boundary was adjusted by the Scottish Adjacent Waters Boundaries Order 1999 so that the boundary within the territorial waters (up to the limit) is north of the boundary for oil installations established by the Civil Jurisdiction (Offshore Activities) Order 1987. The land border is near and roughly parallel to the 420 million-year-old Iapetus Suture.


title: Anglo-Scottish border

text: The border country, historically known as the Scottish Marches, is the area either side of the Anglo-Scottish border including parts of the modern council areas of Dumfries and Galloway and the Scottish Borders, and parts of the English counties of Cumbria and Northumberland. It is a hilly area, with the Scottish Southern Uplands to the north, and the Cheviot Hills forming the border between the two countries to the south. From the Norman conquest of England until the reign of James VI of Scotland, who in the course of his reign became James I of England while retaining the more northerly realm, border clashes were common and the monarchs of both countries relied on Scottish Earls of March and Lord Warden of the Marches to defend and control the frontier region.


title: Anglo-Scottish border

text: In 1333, during the Second War of Scottish Independence, Scotland was defeated at the Battle of Halidon Hill and Edward III occupied much of the borderlands. Edward declared Edward Balliol the new King of Scots, in exchange for the much of southern Scotland and absolute supplication, but this was not recognised by the majority of the Scottish nobility who remained loyal to David II and conflict continued. By 1341, Perth and Edinburgh had been retaken by the Scots and Edward Balliol fled to England, effectively nullifying the supposed treaty. Edward would continue the war but was unable to restore the puppet ruler Balliol to the throne and with the Treaty of Berwick (1357) Scottish independence was once again acknowledged with any pretence to territorial annexations dropped.


title: Anglo-Scottish border

text: A 16th-century Act of the Scottish Parliament talks about the chiefs of the border clans, and a late 17th-century statement by the Lord Advocate uses the terms "clan" and "family" interchangeably. Although Lowland aristocrats may have increasingly liked to refer to themselves as "families", the idea that the term "clan" should be used of Highland families alone is a 19th-century convention.


title: Anglo-Scottish border

text: Historic Border clans include the following: Armstrong, Beattie, Bannatyne, Bell, Briar, Carruthers, Douglas, Elliot, Graham, Hedley of Redesdale, Henderson, Hall, Home or Hume, Irvine, Jardine, Johnstone, Kerr, Little, Moffat, Nesbitt, Ogilvy, Porteous, Routledge, Scott, Thompson, Tweedie.


title: Anglo-Scottish border

text: During late medieval and early modern eras—from the late 13th century, with the creation by Edward I of England of the first Lord Warden of the Marches to the early 17th century and the creation of the Middle Shires, promulgated after the personal union of England and Scotland under James VI of Scotland (James I of England)—the area around the border was known as the Scottish Marches.


title: Anglo-Scottish border

text: For centuries the Marches on either side of the boundary was an area of mixed allegiances, where families or clans switched which country or side they supported as suited their family interests at that time, and lawlessness abounded. Before the personal union of the two kingdoms under James, the border clans would switch allegiance between the Scottish and English crowns depending on what was most favourable for the members of the clan. For a time a powerful local clan dominated a region on the border between England and Scotland. It was known as the Debatable Lands and neither monarch's writ was heeded.


title: Anglo-Scottish border

text: Following the 1603 Union of the Crowns, King James VI & I decreed that the Borders should be renamed 'the Middle Shires'. In the same year the King placed George Home, 1st Earl of Dunbar in charge of pacification of the borders. Courts were set up in the towns of the Middle Shires and known reivers were arrested. The more troublesome and lower classes were executed without trial; known as "Jeddart justice" (after the town of Jedburgh in Roxburghshire). Mass hanging soon became a common occurrence. In 1605 he established a joint commission of ten members, drawn equally from Scotland and England, to bring law and order to the region. This was aided by statutes in 1606 and 1609, first to repeal hostile laws on both sides of the border, and then to more easily prosecute cross-border raiders. Reivers could no longer escape justice by crossing from England to Scotland or vice versa. The rough-and-ready Border Laws were abolished and the folk of the middle shires found they had to obey the law of the land like all other subjects.


title: Anglo-Scottish border

text: In 1607 James felt he could boast that "the Middle Shires" had "become the navel or umbilic of both kingdoms, planted and peopled with civility and riches". After ten years King James had succeeded; the Middle Shires had been brought under central law and order. By the early 1620s the Borders were so peaceful that the Crown was able to scale down its operations.


title: Anglo-Scottish border

text: Despite these improvements, the Joint Commission continued its work, and as late as 25 September 1641 under King Charles I, Sir Richard Graham, a local laird and English MP, was petitioning the Parliament of Scotland "for regulating the disorders in the borders". Conditions along the border generally deteriorated during the Commonwealth and Protectorate periods, with the development of Moss-trooper raiders. Following the Restoration, on-going border lawlessness was dealt with by reviving former legislation, renewed continually in eleven subsequent acts, for periods ranging from five to eleven years, up until the late 1750s.


title: Anglo-Scottish border

text: The Debatable Lands lay between Scotland and England to the north of Carlisle, the largest population centre being Canonbie. For over three hundred years the area was effectively controlled by local clans, such as the Armstrongs, who successfully resisted any attempt by the Scottish or English governments to impose their authority. In 1552 commissioners met to divide the land in two: Douglas of Drumlanrigg leading the Scots; Lord Wharton leading the English; the French ambassador acting as umpire. The Scots' Dike was built as the new frontier, with stones set up bearing the arms of England and of Scotland.


title: Anglo-Scottish border

text: Berwick is famous for its hesitation over whether it is part of Scotland or England. Berwickshire is in Scotland while the town is in England, although both Berwick and the lands up to the Firth of Forth belonged to the Kingdom of Northumbria in the Early Middle Ages. The town changed hands more than a dozen times before being finally taken by the English in 1482, though confusion continued for centuries. The Wales and Berwick Act 1746 clarified the status of Berwick as an English town. In the 1950s the artist Wendy Wood moved the border signs south to the middle of the River Tweed as a protest. In 2008 SNP MSP Christine Grahame made calls in the Scottish Parliament for Berwick to become part of Scotland again. Berwick's MP Anne-Marie Trevelyan has resisted any change, arguing that: "Voters in Berwick-upon-Tweed do not believe it is whether they are in England or Scotland that is important."


title: Anglo-Scottish border

text: At the River Tweed the border runs down the middle of the river, however between the villages of Wark and Cornhill the Scottish border comes south of the river to enclose a small riverside meadow of approximately 2 to 3 acres (about a hectare). This piece of land is known as the Ba Green. It is said locally that every year the men of Coldstream (to the North of the river) would play mob football with the men of Wark (to the South of the river) at Ba, and the winning side would claim the Ba Green for their country. As Coldstream grew to have a larger population than Wark, the Coldstream men always defeated the Wark men at the game, and so the land became a permanent part of Scotland.


title: Anglo-Scottish border

text: It is a common misconception that Hadrian's Wall marks the Anglo-Scottish border. The wall lies entirely within England and has never formed this boundary. While in the west, at Bowness-on-Solway, it is less than south of the border with Scotland, in the east it is as much as away.


title: Anglo-Scottish border

text: For centuries the wall was the boundary between the Roman province of "Britannia" (to the south) and the Celtic lands of "Caledonia" (to the north). However "Britannia" occasionally extended as far north as the later Antonine Wall. Furthermore, to speak of England and Scotland at any time prior to the ninth century is anachronistic; such nations had no meaningful existence during the period of Roman rule.


title: Anglo-Scottish border

text: "Hadrian's Wall" is nonetheless often used as an informal reference to the modern border, often semi-humorously.


title: Anglo-Scottish border

text: Cumbria and Northumberland have amongst the largest Scottish-born communities in the world outside Scotland. 16,628 Scottish-born people were residing in Cumbria in 2001 (3.41% of the county's population) and 11,435 Scottish-born people were residing in Northumberland (3.72% of the county's population); the overall percentage of Scottish-born people in England is 1.62%.


title: Anglo-Scottish border

text: Consequently, almost 9% of Scotland's population is English-born (459,486), with higher than average percentages of English-born people in both Dumfries & Galloway and the Scottish Borders council areas, respectively, reaching as high as 35% or higher English-born.<ref>


title: Evan Mock

text: Evan Mock is an American model, actor, and skateboarder. He is known for starring in the HBO Max series "Gossip Girl".


title: Evan Mock

text: Evan Mock was born in Waimea Bay on Oahu in Hawaii. His mother is Filipino, while his father is American and a surfboard fin maker. Mock was homeschooled. Growing up, he aspired to be a professional surfer or skater. Mock relocated to California at age 18 to professionally skateboard. He rose to prominence after singer Frank Ocean posted a video of him skating.


title: Evan Mock

text: Mock modeled in fashion shows for the brands Louis Vuitton and 1017 Alyx 9SM and launched a clothing line called Sorry in Advance in 2019. He then appeared in advertisements for fragrances by the retailer the Aldo Group and fashion designer Paco Rabanne. Mock starred in a modeling campaign for a clothing collection by fashion designer Giuseppe Zanotti the following year. In June 2021, he launched a collection with the clothing company RVCA. Mock stars as private school student Akeno "Aki" Menzies in the teen drama television series "Gossip Girl", which premiered on HBO Max in July 2021. The series marked his first acting role. Its creator Joshua Safran created the part for Mock to portray.


title: Evan Mock

text: Mock splits his time between Oahu and New York City. Despite playing a character who is exploring his sexuality on "Gossip Girl", Mock is heterosexual. His pink hair has been regarded as his signature look.


title: Eli Goree

text: Eli Goree (born May 26, 1994) is a Canadian actor. He is best known for his roles as Quincy in HBO's "Ballers", Malik in "Da Kink in My Hair" (2007–2009), Wells Jaha in the post-apocalyptic drama show "The 100" (2014–2017), Joel Goodson in the supernatural horror show "Dead of Summer", and Cassius Clay in Regina King's biographical drama film "One Night in Miami..." (2020). In 2018, he started a recurring role on the CW's TV series "Riverdale", where he plays Munroe "Mad Dog" Moore.


title: Eli Goree

text: Goree grew up in Halifax, Nova Scotia. He was raised by a single mother. He began his acting career at age six in "Sesame Park", the Canadian version of "Sesame Street". In 2003, he hosted "The Big Black Rap Show" on the Dalhousie University campus radio station CKDU-FM. In 2006, he became one of the hosts for the last season of the CBC TV series "Street Cents". In the same year, he also began working as a freelancing journalist for "Canada Now".


title: Eli Goree

text: From 2007 to 2009, he was cast as Malik in popular Global TV series "Da Kink in My Hair". He also appeared in the Vision TV series "Soul".


title: Eli Goree

text: On stage, Goree played the lead role of Jake in the 2009 critically acclaimed play "Secrets of a Black Boy".


title: Eli Goree

text: Between 2010 and 2013, he appeared in the mockumentary "Pure Pwnage" as well as guest roles in The CW's fantasy horror series "Supernatural", The CW's medical drama "Emily Owens, M.D.", Showcase's sci-fi miniseries "Eve of Destruction" and CTV's police crime drama "Motive".


title: Eli Goree

text: In 2014, he was cast as Wells Jaha, one of the main characters in the first season of The CW's post-apocalyptic drama show "The 100".


title: Eli Goree

text: He appeared as Conner, an amputee war veteran, in the Amazon Prime Video science fiction series "The Peripheral".


title: Valerie Biden Owens

text: Valerie Biden Owens (November 5, 1945) is an American political strategist, campaign manager and former educator. She is the younger sister of Joe Biden, the 46th and current President of the United States. In 2016, president Barack Obama nominated her Alternate Representative of the United States to the 71st Session of the General Assembly of the United Nations.


title: Valerie Biden Owens

text: Owens has played a substantial role in all of her brother's political campaigns. She was the campaign manager during all of his Senate elections and for his 1988 and 2008 presidential campaigns, as well as a senior advisor to his successful 2020 presidential campaign. Owens published her autobiography, "Growing Up Biden", in 2022.


title: Valerie Biden Owens

text: She was born the daughter of Catherine Eugenia "Jean" (née Finnegan; 1917–2010) and Joseph Robinette Biden Sr. (1915–2002). Her brothers are Joe, Francis "Frank" Biden, and James "Jim" Biden. Her family is of Irish Catholic background. Biden's father was initially wealthy, but later suffered several financial setbacks; for several years the family lived with Biden's maternal grandparents in Scranton, Pennsylvania. Joe Biden Sr. later became a successful used car salesman, maintaining the family a middle-class lifestyle.


title: Valerie Biden Owens

text: Owens graduated from Ursuline Academy in Wilmington, Delaware in 1963, and went on to study at the University of Delaware, where she was on the dean's list and was homecoming queen, graduating in 1967.


title: Valerie Biden Owens

text: From 1997 until 2016, she served as executive vice-president of Joe Slade White & Company, a media consultant firm. Owens has worked with the service organization Ministry of Caring for over 35 years and sits on their Board of Directors.


title: Valerie Biden Owens

text: She has worked extensively with Women's Campaign International to help teach women how to develop and grow their political skills. In 2013, Owens traveled with her brother Joe Biden to the Vatican City as an official U.S. delegate for the inauguration of Pope Francis.


title: Valerie Biden Owens

text: In 2014, Owens was a Resident Fellow at the Harvard Institute of Politics. In 2017, Owens was a featured speaker at a Ted Talk conference in Wilmington, Delaware. Owens is vice-chair of both the Biden Institute at the University of Delaware and the Biden Foundation. Owens returns to the University of Delaware periodically to give lectures on politics and her experiences as a woman on the campaign trail.


title: Valerie Biden Owens

text: She has traveled around the world as a motivational speaker, and teacher of leadership and communication seminars. She helped to found the Owens-Patrick seminar group. Owens currently sits on the advisory board for the University of Nevada, Las Vegas Public Policy Institute.


title: Valerie Biden Owens

text: Owens has played a substantial role in all of her brother's political campaigns dating back to his first campaign, for the New Castle County, Delaware council in 1970. Owens managed for Joe Biden's 1988 presidential campaign. In 2008, Owens and Ashley Judd campaigned together in North Carolina at several events in support of Barack Obama and Joe Biden.


title: Valerie Biden Owens

text: Joe Biden mentioned her in his presidential acceptance speech on November 7, 2020. Owens was in attendance at the event in Wilmington, Delaware, where she also met Maya Harris, the sister of Vice President-elect Kamala Harris.


title: Valerie Biden Owens

text: Owens' first husband was Bruce Saunders, whom she married shortly after graduating college. Bruce and Valerie moved in with Joe Biden and his two sons, Hunter and Beau, following the death of her sister-in-law Neilia in a car crash in December 1972. Valerie helped look after her nephews so that Joe could begin his first term as senator in 1973. Valerie and Bruce had both worked on Joe Biden's first Senate campaign in 1972.


title: Valerie Biden Owens

text: Owens is married to attorney John T. Owens, with whom she has three children: son Cuffe Owens, also an attorney, and two daughters, Missy Owens and Casey Owens Castello. John T. Owens was a friend of Joe Biden's during their law school years at Syracuse University. The two were wed in a Roman Catholic ceremony at the Church Center for the United Nations in 1975.


title: Valerie Biden Owens

text: In 2021, Forbes listed Owens on their Impact List of 50 Women over 50 who are inspiring change in their communities through social entrepreneurship, law, advocacy and education.


title: Golf course

text: A golf course is the grounds on which the sport of golf is played. It consists of a series of holes, each consisting of a tee box, a fairway, the rough and other hazards, and a green with a cylindrical hole in the ground, known as a "cup". The cup holds a flagstick, known as a "pin". A standard round of golf consists of 18 holes, and as such most courses contain 18 distinct holes; however, there are many 9-hole courses and some that have holes with shared fairways or greens. There are also courses with a non-standard number of holes, such as 12 or 14.


title: Golf course

text: The vast majority of golf courses have holes of varying length and difficulties that are assigned a standard score, known as par, that a proficient player should be able to achieve; this is usually three, four or five strokes. Par-3 courses consist of holes all of which have a par of three. Short courses have gained in popularity; these consist of mostly par 3 holes, but often have some short par 4 holes.


title: Golf course

text: Many older courses are links, often coastal. The first golf courses were based on the topography of sand dunes and dune slacks with a ground cover of grasses, exposed to the wind and sea. Courses are private, public, or municipally owned, and typically feature a pro shop. Many private courses are found at country clubs.


title: Golf course

text: Although a specialty within landscape design or landscape architecture, golf course architecture is considered a separate field of study. Some golf course architects become celebrities in their own right, such as Alister MacKenzie; others are professional golfers of high standing and demonstrated appreciation for golf course composition, such as Jack Nicklaus. The field is partially represented by the American Society of Golf Course Architects, the European Institute of Golf Course Architects, and the Society of Australian Golf Course Architects, although many of the finest golf course architects in the world choose not to become members of any such group, as associations of architects are not government-sanctioned licensing bodies, but private groups. While golf courses often follow the original landscape, some modification is unavoidable. This is increasingly the case as new courses are more likely to be sited on less optimal land. Bunkers and sand traps are always built in by architects unless the formation of such items is already in the course's natural terrain.


title: Golf course

text: The layout of a course follows certain traditional principles, such as the number of holes (nine and 18 being most common), their par values, and the number of holes of each par value per course. It is also preferable to arrange greens to be close to the tee box of the next playable hole, to minimize travel distance while playing a round, and to vary the mix of shorter and longer holes. Combined with the need to package all the fairways within what is frequently a compact square or rectangular plot of land, the fairways of a course tend to form an oppositional tiling pattern. In complex areas, two holes may share the same tee box, fairway, or even green. It is also common for separate tee-off points to be positioned for men, women, and amateurs, each one respectively lying closer to the green. Eighteen-hole courses are traditionally broken down into a "front 9" (holes 1–9) and a "back 9" (holes 10–18). On older courses (especially links courses, like the Old Course at St. Andrews), the holes may be laid out in one long loop, beginning and ending at the clubhouse, and thus the front 9 is referred to on the scorecard as "out" (heading out away from clubhouse) and the back 9 as "in" (heading back in toward the clubhouse). More recent courses (and especially inland courses) tend to be routed with the front 9 and the back 9 each constituting a separate loop beginning and ending at the clubhouse. This is partly for the convenience of the players and the club, as then it is easier to play just a 9-hole round, if preferred, or stop at the clubhouse for a snack between the front 9 and the back 9.


title: Golf course

text: A successful design is as visually pleasing as it is playable. With golf being a form of outdoor recreation, the strong designer is an adept student of natural landscaping who understands the aesthetic cohesion of vegetation, water bodies, paths, grasses, stonework, and woodwork, among other elements.


title: Golf course

text: Most golf courses have only par-3, −4, and −5 holes, although some courses include par-6 holes. The Ananti CC and the Satsuki golf course in Sano, Japan, are the only courses with par-7 holes.


title: Golf course

text: Par is primarily determined by the playing length of each hole from the teeing ground to the putting green. Holes are generally assigned par values between three and five, which includes a regulation number of strokes to reach the green based on the average distance a proficient golfer hits the ball, and two putts. On occasion, factors other than distance are taken into account when setting the par for a hole; these include altitude, terrain and obstacles that result in a hole playing longer or shorter than its measured distance, e.g. route is significantly uphill or downhill, or requiring play of a stroke to finish short of a body of water before hitting over it.


title: Golf course

text: Under the United States Golf Association, the typical distances for the various holes from standard tees are as follows:


title: Golf course

text: The first section of every hole consists of the teeing ground, or tee-box. There is typically more than one available box where a player places his ball, each one a different distance from the hole (and possibly with a different angle of approach to the green or fairway) to provide differing difficulty. The teeing ground is generally as level as feasible, with closely mown grass very similar to that of a putting green, and most are slightly raised from the surrounding fairway.


title: Golf course

text: Each tee box has two markers showing the bounds of the legal tee area. The teeing area spans the distance between the markers, and extends two-club lengths behind the markers. A golfer may play the ball standing outside the teeing area, but the ball itself must be placed and struck from within the area. A golfer may place his ball directly on the surface of the teeing ground (called hitting it "off the deck"), or the ball may be supported by a manufactured tee (limited to a height of four inches), or by any natural substance, such as a mound of sand placed on the teeing surface.


title: Golf course

text: After the first shot from the tee ("teeing off"), the player whose ball is farthest from the green hits the ball from where it came to rest; this spot is known as its "lie". When the ball is in play and not out of bounds or in a hazard the player must play the ball as it lies. The area between the tee box and the putting green where the grass is cut even and short is called the "". The area between the fairway and the out-of-bounds markers, and also between a mowed apron surrounding the green and out of bounds, is the "rough"; the grass there is cut higher and is often of a coarser strain than on the fairways, making roughs disadvantageous areas from which to hit. On par-3 holes, the player is expected to be able to drive the ball to the green on the first shot from the tee box. On holes longer than par 3, players are expected to require at least one additional shot to reach their greens.


title: Golf course

text: While many holes are designed with a direct line-of-sight from the teeing ground to the green, a hole may bend either to the left or to the right. This is called a "dogleg", in reference to the similarity to a dog's ankle. The hole is called a "dogleg left" if the hole angles leftwards, and a "dogleg right" if the hole angles rightwards. A hole's direction may bend twice, which is called a "double dogleg".


title: Golf course

text: Just as there are good-quality grasses for putting greens, there are good-quality grasses for the fairway and rough. The quality of grass influences the roll of the ball as well as the ability of the player to "take a divot" (effectively, the ability to hit down into the ball, hitting the ball first, then hitting the turf and removing a portion of it as the club continues its arc). Fairways on prestigious tours, like the PGA Tour, are cut low. Mowing heights influence the play of the course. For example, the grass heights at U.S. Open events are alternated from one hole to the next in order to make the course more difficult. One example of this is the infamous roughs at U.S. Opens, which are often 3 to 5 inches high, depending on how close to the fairway or green the section of grass will be. This makes it difficult for a player to recover after a bad shot.


title: Golf course

text: Variants of grass used for fairways and roughs include bent grass, Tifway 419 Bermuda grass, rye grass, Kentucky bluegrass, and Zoysiagrass. As in putting-green grass types, not every grass type works equally well in all climate types.


title: Golf course

text: The "putting green", or simply the "green", is an area of very closely trimmed grass on relatively even, smooth ground surrounding the hole, allowing players to make precision strokes on it. To "putt" is to play a stroke on this surface, usually with the eponymous "putter" club, which has very low loft so that the ball rolls smoothly along the ground, and hopefully into the cup. The shape and topology of the green can vary almost without limit, but for practical purposes the green is usually flatter than other areas of the course, though gentle slopes and undulations can add extra challenge to players who must account for these variations in their putting line. The green typically does not include any fully enclosed hazards such as sand or water; however, these hazards can often adjacent to the green, and depending on the shape of the green and surrounding hazards, and the location of the hole (which often changes from day to day to promote even wear of the turf of the green), there may not be a direct putting line from a point on the green to the cup.


title: Golf course

text: Golfers use a method known as "reading" the green to enhance their chances of making a putt. Reading a green involves determining the speed, grain, incline, decline and tilt of the green on the line of the putt. Most putts are not struck directly at the hole, instead they must be struck to take into account the characteristics of the green to arrive at the hole at the proper angle and speed. The best players will read the green by walking around the green and studying the characteristics of the green before addressing the ball. Reading the green and putting are considered by many golfers to be the most difficult part of the game.


title: Golf course

text: The green is typically surrounded by slightly higher grass, cut at a height between that of the green and fairway, and then by the fairway and/or rough. This longer grass surrounding the green is known as the "fringe" and is designed to slow and stop balls rolling along the green from an approach shot or errant putt, preventing them from exiting the green. Though putting strokes can be made on it, the higher grass can interfere with the path of the ball, so players often choose to use a lofted club such as an iron to make a "chip shot" or a "bump and run", where the ball carries in the air for a few yards and then rolls along the green like a normal putt.


title: Golf course

text: The grass of the putting green (more commonly just "green") is cut very short so that a ball can roll for a long distance. The most common types of greens are for cold winter, but warmer summer regions (i.e., not extremely warm, as in the Southern and Southwestern United States) are bent grass greens. A green may consist of a thin carpet so that bad weather is not allowed to become a serious factor in maintaining the course. These are considered the best greens because they may be cut to an extremely low height, and because they may be grown from seed. Bent grass does not have grain, which makes it superior as a putting surface. However, bent grass may become infested with "poa annua", a costly and time-consuming weed. Augusta National is one of many golf courses to use this type of green. The original design of Augusta National did not include bent grass greens, but in the 1980s the controversial decision was made to convert the greens from Bermuda to bent grass. This has affected the speed and playing of Augusta National. Many other golf courses subsequently made the decision to change from Bermuda to bent grass when they observed increased business at courses that had already changed over.


title: Golf course

text: Another type of grass common for greens is TifDwarf Hybrid Bermuda (other variants exist, but TifDwarf is one of the most common), or simply Bermuda grass. Bermuda is more common in regions that have very warm summers and mild winters, such as the Southern and Southwestern United States. Red Bridge Golf Course was the first course in North Carolina to utilize a special Bermuda called Mini Verde. A green is generally established from sod which has had the soil washed off of it (to avoid soil compatibility problems) and which is then laid tightly over the green, then rolled and topdressed with fine sand. Another common and more economical approach for establishing a putting green is to introduce hybrid Bermuda sprigs (the stolon of the grass which are raked out at the sod farm), which are laid out on the green.


title: Golf course

text: Two downside factors of Bermuda greens are cost of maintenance, and also the existence of grain (the growth direction of the blades of grass), which affects the ball's roll and which is called "the grain of the green" and not to be confused with "the rub of the green" which are idiosyncrasies encountered getting through the hole. The slope or break of the green also affects the roll of the ball. The hole, or cup, is always found within the green and must have a diameter of and a depth of at least . Its position on the green is not fixed and typically is changed daily by a greenskeeper in order to prevent excessive localized wear and damage to the turf. A new hole will be cut by a device that removes a plug of the turf from the ground, and the reinforced cup is then moved, before the old hole is filled in with the plug cut from the new hole and levelled. The hole has a flag on a pole positioned in it so that it may be seen from a distance, but not necessarily from the tee. This location marker is officially called the "flagstick" but is also commonly referred to as the "pin". Flagsticks are made of either coated fiberglass, metal, or wood and have a metal or synthetic bottom (called a ferrule) that is designed to fit in the hole cup.


title: Golf course

text: Putting greens are not all of the same quality. The finest-quality greens are well-kept so that a ball will roll smoothly over the closely mowed grass. Excess water can be removed from a putting green using a machine called a water hog. Golfers describe a green as "fast" if a light stroke on the ball makes it roll a long distance; conversely, on a "slow" green a stronger stroke is necessary to roll the ball the same distance. The exact speed of a green can be determined with a stimp meter. By collecting sample measurements, golf courses can be compared in terms of average green speed. It is, however, illegal by the rules of golf to test the speed of a green while playing by rolling a ball on it, or by feeling or rubbing the green.


title: Golf course

text: The cost of installing and maintaining grass greens constitutes a considerable proportion of the expense of installing and maintaining a golf course. To save money, many low budget courses catering to casual players have sand greens instead of real grass. In recent years, artificial turf has also become an increasingly popular surface as a less costly alternative to grass which more closely resembles the appearance and feel of real grass compared to a sand surface.


title: Golf course

text: Holes often include hazards, which are special areas that have additional rules for play, and are generally of two types: (1) water hazards, such as ponds, lakes, and rivers; and (2) bunkers, or sand traps.


title: Golf course

text: Special rules apply to playing a ball that falls in a hazard. For example, a player may not touch the ground or water with their club before playing the ball, not even for a practice swing. A ball in any hazard may be played as it lies without penalty. If it cannot be played from the hazard, the ball may be hit from another location, generally with a penalty of one stroke. The Rules of Golf specify exactly the point from which the ball may be played outside a hazard. Bunkers are small to medium areas, usually lower than the fairway but of varying topography, that are filled with sand and generally incorporate a raised lip or barrier. It is more difficult to play the ball from sand than from grass, as the ball may embed itself into the sand, and the loose nature of the sand and more severe sloping of many bunkers make taking one's stance more difficult. As in any hazard, a ball in a bunker must be played without touching the sand with the club except during the stroke, and loose impediments (leaves, stones, twigs) must not be moved before making the stroke.


title: Golf course

text: Courses may also have other design features which the skilled player will avoid; there are earth bunkers (pits or depressions in the ground that are not filled with sand but require a lofted shot to escape), high grass and other dense vegetation, trees or shrubs, ravines and other rocky areas, steep inclines, etc.; while disadvantageous to play from, these are typically not considered "hazards" unless specifically designated so by the course (a ravine or creekbed may be termed a "water hazard" even if completely dry)


title: Golf course

text: Often, a golf course will include among its facilities a practice range or driving range, usually with practice greens, bunkers, and driving areas. Markers showing distances are usually included on a practice range for the golfer's information. Driving ranges are also commonly found as separate facilities, unattached to a golf course, where players may simply hit balls into the range for practice or enjoyment.