query: what inspired m.c. escher to become an artist?

title: M. C. Escher

text: attitude to intellectuality and lyricism, but this did not rehabilitate Escher, because traditional critics still disliked his narrative themes and his use of perspective. However, these same qualities made his work highly attractive to the public. Escher is not the first artist to explore mathematical themes: Parmigianino (1503–1540) had explored spherical geometry and reflection in his 1524 "Self-portrait in a Convex Mirror", depicting his own image in a curved mirror, while William Hogarth's 1754 "Satire on False Perspective" foreshadows Escher's playful exploration of errors in perspective. Another early artistic forerunner is Giovanni Battista Piranesi (1720–1778), whose dark "fantastical" prints such

title: M. C. Escher

text: M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for long somewhat neglected in the art world; even in his native Netherlands; he was 70 before a retrospective exhibition was held. In the twenty-first century, he became more widely appreciated, with exhibitions across the world. His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability,

title: Puddle (M. C. Escher)

text: soft and muddy and in it there are two distinctly different sets of tire tracks, two sets of footprints going in opposite directions and two bicycle tracks. Escher has thus captured three elements: the water, sky and earth. Puddle (M. C. Escher) Puddle is a woodcut print by the Dutch artist M. C. Escher, first printed in February 1952. Since 1936, Escher’s work had become primarily focused on paradoxes, tessellation and other abstract visual concepts. This print, however, is a realistic depiction of a simple image that portrays two perspectives at once. It depicts an unpaved road with a large

title: Puddle (M. C. Escher)

text: Puddle (M. C. Escher) Puddle is a woodcut print by the Dutch artist M. C. Escher, first printed in February 1952. Since 1936, Escher’s work had become primarily focused on paradoxes, tessellation and other abstract visual concepts. This print, however, is a realistic depiction of a simple image that portrays two perspectives at once. It depicts an unpaved road with a large pool of water in the middle of it at twilight. Turning the print upside-down and focusing strictly on the reflection in the water, it becomes a depiction of a forest with a full moon overhead. The road is

title: Belvedere (M. C. Escher)

text: Escher as a lithograph in 1935. The ridge in the background is part of Morrone Mountains in Abruzzo, that Escher had visited several times when living in Italy during the 1920s and 1930s. In 2012, Prof. Gershon Elber of Israel's Technion University, using specially designed CAD software and a 3D printer, created a 3D model of Belvedere and other impossible Escher structures, viewable only from one angle. Belvedere (M. C. Escher) Belvedere is a lithograph print by the Dutch artist M. C. Escher, first printed in May 1958. It shows a plausible-looking belvedere building that is an impossible object, modelled

title: Dragon (M. C. Escher)

text: copy of this print is in the collections of U.S. National Gallery of Art and the National Gallery of Canada. Dragon (M. C. Escher) Dragon () is a wood engraving print created by Dutch artist M. C. Escher in April 1952, depicting a folded paper dragon perched on a pile of crystals. It is part of a sequence of images by Escher depicting objects of ambiguous dimension, including also "Three Spheres I", "Doric Columns", "Drawing Hands" and "Print Gallery". Escher wrote "this dragon is an obstinate beast, and in spite of his two-dimensions he persists in assuming that he has

title: Dragon (M. C. Escher)

text: Dragon (M. C. Escher) Dragon () is a wood engraving print created by Dutch artist M. C. Escher in April 1952, depicting a folded paper dragon perched on a pile of crystals. It is part of a sequence of images by Escher depicting objects of ambiguous dimension, including also "Three Spheres I", "Doric Columns", "Drawing Hands" and "Print Gallery". Escher wrote "this dragon is an obstinate beast, and in spite of his two-dimensions he persists in assuming that he has three". Two slits in the paper from which the dragon is folded open up like kirigami, forming holes that make

title: Waterfall (M. C. Escher)

text: Waterfall (M. C. Escher) Waterfall () is a lithograph by the Dutch artist M. C. Escher, first printed in October 1961. It shows a perpetual motion machine where water from the base of a waterfall appears to run downhill along the water path before reaching the top of the waterfall. While most two-dimensional artists use relative proportions to create an illusion of depth, Escher here and elsewhere uses conflicting proportions to create a visual paradox. The watercourse supplying the waterfall (its aqueduct or leat) has the structure of two Penrose triangles. A Penrose triangle is an impossible object designed by

title: Belvedere (M. C. Escher)

text: Belvedere (M. C. Escher) Belvedere is a lithograph print by the Dutch artist M. C. Escher, first printed in May 1958. It shows a plausible-looking belvedere building that is an impossible object, modelled after an impossible cube. In this lithograph, Escher uses two-dimensional images to depict objects free of the confines of the three-dimensional world. The image is of a rectangular three-story building. The upper two floors are open at the sides with the top floor and roof supported by pillars. From the viewer's perspective, all the pillars on the middle floor are the same size at both the front

title: Print Gallery (M. C. Escher)

text: Print Gallery (M. C. Escher) Print Gallery () is a lithograph printed in 1956 by the Dutch artist M. C. Escher. It depicts a man in a gallery viewing a print of a seaport, and among the buildings in the seaport is the very gallery in which he is standing, making use of the Droste effect with visual recursion. The lithograph has attracted discussion in both mathematical and artistic contexts. Bruno Ernst cites M. C. Escher as stating that he began "Print Gallery" "from the idea that it must be possible to make an annular bulge, a cyclic expansion ...

title: Stars (M. C. Escher)

text: of the Rijksmuseum, National Gallery of Art, Mildred Lane Kemper Art Museum, Boston Public Library, and the National Gallery of Canada. Stars (M. C. Escher) Stars is a wood engraving print created by the Dutch artist M. C. Escher in 1948, depicting two chameleons in a polyhedral cage floating through space. Although the compound of three octahedra used for the central cage in "Stars" had been studied before in mathematics, it was most likely invented independently for this image by Escher without reference to those studies. Escher used similar compound polyhedral forms in several other works, including "Crystal" (1947), "Study

title: Stars (M. C. Escher)

text: Stars (M. C. Escher) Stars is a wood engraving print created by the Dutch artist M. C. Escher in 1948, depicting two chameleons in a polyhedral cage floating through space. Although the compound of three octahedra used for the central cage in "Stars" had been studied before in mathematics, it was most likely invented independently for this image by Escher without reference to those studies. Escher used similar compound polyhedral forms in several other works, including "Crystal" (1947), "Study for Stars" (1948), "Double Planetoid" (1949), and "Waterfall" (1961). The design for "Stars" was likely influenced by Escher's own interest in

title: M. C. Escher

text: Spheres"; E. H. Gombrich's "Meditations on a Hobby Horse" with "Horseman"; Pamela Hall's "Heads You Lose" with "Plane Filling 1"; Patrick A. Horton's "Mastering the Power of Story" with "Drawing Hands"; Erich Gamma et al.'s "Design Patterns: Elements of Reusable Object-oriented software" with "Swans"; and Arthur Markman's "Knowledge Representation" with "Reptiles". The "World of Escher" markets posters, neckties, T-shirts, and jigsaw puzzles of Escher's artworks. Both Austria and the Netherlands have issued postage stamps commemorating the artist and his works. M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who

title: Waterfall (M. C. Escher)

text: known as Escher's solid. Below the mill is a garden of bizarre, giant plants. This is actually a magnified view of a cluster of moss and lichen that Escher drew in ink as a study in 1942. The background seems to be a climbing expanse of terraced farmland. Waterfall (M. C. Escher) Waterfall () is a lithograph by the Dutch artist M. C. Escher, first printed in October 1961. It shows a perpetual motion machine where water from the base of a waterfall appears to run downhill along the water path before reaching the top of the waterfall. While most

title: Reptiles (M. C. Escher)

text: notebook), and re-integration (matches and cigarettes symbolizing controlled/civilized fire that nonetheless consumes and returns the physical to the abstract). Once a woman telephoned Escher and told him that she thought the image was a "striking illustration of reincarnation". A colorized version of the lithograph was used by rock band Mott the Hoople as the sleeve artwork for its eponymous first album, released in 1969. Reptiles (M. C. Escher) Reptiles is a lithograph print by the Dutch artist M. C. Escher first printed in March 1943. It depicts a desk upon which is a 2D drawing of a tessellated pattern of

title: Relativity (M. C. Escher)

text: to lead to basements below the parks. Though physically possible, such basements are certainly unusual and add to the surreal effect of the picture. This is one of Escher’s most popular works and has been used in a variety of ways. Relativity (M. C. Escher) Relativity is a lithograph print by the Dutch artist M. C. Escher, first printed in December 1953. The first version of this work was a woodcut earlier that same year. It depicts a world in which the normal laws of gravity do not apply. The architectural structure seems to be the centre of an idyllic

title: Relativity (M. C. Escher)

text: Relativity (M. C. Escher) Relativity is a lithograph print by the Dutch artist M. C. Escher, first printed in December 1953. The first version of this work was a woodcut earlier that same year. It depicts a world in which the normal laws of gravity do not apply. The architectural structure seems to be the centre of an idyllic community, with most of its inhabitants casually going about their ordinary business, such as dining. There are windows and doorways leading to park-like outdoor settings. All of the figures are dressed in identical attire and have featureless bulb-shaped heads. Identical characters

title: Another World (M. C. Escher)

text: "Cosmicomics". Another World (M. C. Escher) Another World II, also known as Other World II, is a woodcut print by the Dutch artist M. C. Escher first printed in January 1947. It depicts a cubic architectural structure made from brick. The structure is a paradox with an open archway on each of the five visible sides of the cube. The structure wraps around the vertical axis to enclose the viewer's perspective. At the bottom of the image is an archway which we seem to be looking up from the base, and through it we can see space. At the top

title: Another World (M. C. Escher)

text: Another World (M. C. Escher) Another World II, also known as Other World II, is a woodcut print by the Dutch artist M. C. Escher first printed in January 1947. It depicts a cubic architectural structure made from brick. The structure is a paradox with an open archway on each of the five visible sides of the cube. The structure wraps around the vertical axis to enclose the viewer's perspective. At the bottom of the image is an archway which we seem to be looking up from the base, and through it we can see space. At the top of

title: Reptiles (M. C. Escher)

text: Reptiles (M. C. Escher) Reptiles is a lithograph print by the Dutch artist M. C. Escher first printed in March 1943. It depicts a desk upon which is a 2D drawing of a tessellated pattern of reptiles and hexagons. The reptiles at one edge of the drawing emerge into three dimensional reality, come to life and appear to crawl over a series of symbolic objects (a book on nature, a geometers triangle, a three dimensional/pentagonal dodecahedron, a pewter bowl containing a box of matches and a box of cigarettes) to eventually re-enter the drawing at its opposite edge. Other objects

title: Castrovalva (M. C. Escher)

text: Castrovalva (M. C. Escher) Castrovalva is a lithograph print by the Dutch artist M. C. Escher, first printed in February 1930. Like many of Escher's early works, it depicts a place that he visited on a tour of Italy. It depicts the Abruzzo village of Castrovalva, which lies at the top of a sheer slope. The perspective is toward the northwest, from the narrow trail on the left which, at the point from which this view is seen, makes a hairpin turn to the right, descending to the valley. In the foreground at the side of the trail, there are

title: Snakes (M. C. Escher)

text: for the cover of his 1998 album "György Ligeti: Complete Piano Music, Volume 2". Snakes (M. C. Escher) Snakes is a woodcut print by the Dutch artist M. C. Escher first printed in July 1969. It depicts a disc made up of interlocking circles that grow progressively smaller towards the center and towards the edge. There are three snakes laced through the edge of the disc. "Snakes" has rotational symmetry of order 3, comprising a single wedge-shaped image repeated three times in a circle. This means that it was printed from three blocks that were rotated on a pin to

title: Snakes (M. C. Escher)

text: Snakes (M. C. Escher) Snakes is a woodcut print by the Dutch artist M. C. Escher first printed in July 1969. It depicts a disc made up of interlocking circles that grow progressively smaller towards the center and towards the edge. There are three snakes laced through the edge of the disc. "Snakes" has rotational symmetry of order 3, comprising a single wedge-shaped image repeated three times in a circle. This means that it was printed from three blocks that were rotated on a pin to make three impressions each. Close inspection reveals the central mark left by the pin.

title: Gravitation (M. C. Escher)

text: turtle directly opposite its counterpart. Gravitation (M. C. Escher) Gravitation (also known as Gravity) is a mixed media work by the Dutch artist M. C. Escher completed in June 1952. It was first printed as a black-and-white lithograph and then coloured by hand in watercolour. It depicts a nonconvex regular polyhedron known as the small stellated dodecahedron. Each facet of the figure has a trapezoidal doorway. Out of these doorways protrude the heads and legs of twelve turtles without shells, who are using the object as a common shell. The turtles are in six coloured pairs (red, orange, yellow, magenta,

title: Gravitation (M. C. Escher)

text: Gravitation (M. C. Escher) Gravitation (also known as Gravity) is a mixed media work by the Dutch artist M. C. Escher completed in June 1952. It was first printed as a black-and-white lithograph and then coloured by hand in watercolour. It depicts a nonconvex regular polyhedron known as the small stellated dodecahedron. Each facet of the figure has a trapezoidal doorway. Out of these doorways protrude the heads and legs of twelve turtles without shells, who are using the object as a common shell. The turtles are in six coloured pairs (red, orange, yellow, magenta, green and indigo) with each

title: Castrovalva (M. C. Escher)

text: several flowering plants, grasses, ferns, a beetle and a snail. In the expansive valley below there are cultivated fields and two more towns, the nearest of which is Anversa degli Abruzzi, with Casale in the distance. Castrovalva (M. C. Escher) Castrovalva is a lithograph print by the Dutch artist M. C. Escher, first printed in February 1930. Like many of Escher's early works, it depicts a place that he visited on a tour of Italy. It depicts the Abruzzo village of Castrovalva, which lies at the top of a sheer slope. The perspective is toward the northwest, from the narrow

title: Magic Mirror (M. C. Escher)

text: Magic Mirror (M. C. Escher) Magic Mirror is a lithograph print by the Dutch artist M. C. Escher first printed in January, 1946. It depicts a mirror standing vertically on wooden supports on a tiled surface. The perspective is looking down at an angle at the right hand side of the mirror. There is a sphere at each side of the mirror. The main focus of the image is a procession of small griffin (winged lion) sculptures that emerge from the surface of the mirror and trail away from it in single file. Both the angular reflection of the tiles

title: M. C. Escher in popular culture

text: between Mike Allred's Madman and Bernie Mireault's The Jam, features Escher as a central character when the two characters enter into an alternate universe created by a somewhat godlike Escher, based on many of his works. In 2006 Audi released a commercial with many Escher-inspired scenes. The bonus stages of the first "Sonic the Hedgehog" game, for the Sega Genesis/Mega Drive, feature an animated background of birds turning into fish, a reference to "Sky and Water I". Monument Valley and its sequel features puzzles that are loosely based on Escher's works. M. C. Escher in popular culture There are numerous

title: Magic Mirror (M. C. Escher)

text: and the offset between the reflection of the sphere in front of the mirror and the sphere behind it prove it is a mirror. Yet the reflection of the griffin procession continues to emerge from behind the mirror. The griffin processions of both sides loop around to the front and enter a tessellated pattern on the tile surface. Magic Mirror (M. C. Escher) Magic Mirror is a lithograph print by the Dutch artist M. C. Escher first printed in January, 1946. It depicts a mirror standing vertically on wooden supports on a tiled surface. The perspective is looking down at

title: The Bridge (M. C. Escher)

text: The Bridge (M. C. Escher) The Bridge is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1930. It depicts a bridge connecting two sheer cliffs. On the top of the left hand cliff is a city. The chasm between the two cliffs is narrow but plummets out of view. In the distance is another outcrop with a city built on top. Both the rock and the architecture on this third outcrop are darker in colouration than in the foreground. The buildings appear to be modelled partly after southern Italian architecture. The rock is in

title: The Bridge (M. C. Escher)

text: blocky formations that appeared often during Escher's Italian period and it is possible that the village seen is Assisi. The Bridge (M. C. Escher) The Bridge is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1930. It depicts a bridge connecting two sheer cliffs. On the top of the left hand cliff is a city. The chasm between the two cliffs is narrow but plummets out of view. In the distance is another outcrop with a city built on top. Both the rock and the architecture on this third outcrop are darker in colouration

title: M. C. Escher

text: with Escher's intuitive grasp of mathematics. Inspired by "Relativity", Penrose devised his tribar, and his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches of both objects to Escher, and the cycle of invention was closed when Escher then created the perpetual motion machine of "Waterfall" and the endless march of the monk-figures of "Ascending and Descending". In 1957, Coxeter obtained Escher's permission to use two of his drawings in his paper "Crystal symmetry and its generalizations". He sent Escher a copy of the paper; Escher recorded that Coxeter's figure of a hyperbolic tessellation "gave me quite a

title: Tower of Babel (M. C. Escher)

text: Tower of Babel (M. C. Escher) Tower of Babel is a 1928 woodcut by M. C. Escher. It depicts the Babylonians attempting to build a tower to reach God, a story that is recounted in Genesis 11:9. God frustrated their attempts by creating a confusion of languages so the builders could no longer understand each other and the work halted. Although Escher dismissed his works before 1935 as of little or no value as they were "for the most part merely practice exercises", some of them, including the "Tower of Babel", chart the development of his interest in perspective and

title: Tower of Babel (M. C. Escher)

text: unusual viewpoints that would become the hallmarks of his later, more famous, work. In contrast to many other depictions of the biblical story, such as those by Pieter Brueghel the Elder ("The Tower of Babel") and Gustave Doré ("The Confusion of Tongues"), Escher depicts the tower as a geometrical structure and places the viewpoint above the tower. This allows him to exercise his skill with perspective, but he also chose to centre the picture around the top of the tower as the focus for the climax of the action. He later commented: Tower of Babel (M. C. Escher) Tower of

title: M. C. Escher in popular culture

text: been released, some of which are more or less inspired by the art of M.C. Escher. Some games borrow the graphical art style; some games contain game mechanics that are heavily influenced by the artist while others are simply put tributes to the works of M.C. Escher. In the video "Around the World" (1997) of Daft Punk, men and women, dressed like mummies similar to those in Escher’s painting, perpetually walk around on a stair. "Escher," a song on Teenage Fanclub's album "Thirteen", with lyrics that deal with disorientation. Andrew Lipson created a Lego version of "Relativity". In 1981, Austria

title: Gödel, Escher, Bach

text: mainly about translation. Gödel, Escher, Bach Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic

title: Gödel, Escher, Bach

text: Gödel, Escher, Bach Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even

title: M. C. Escher

text: return for making drawings of their ships, they surprisingly agreed, and he sailed the Mediterranean, becoming interested in order and symmetry. Escher described this journey, including his repeat visit to the Alhambra, as "the richest source of inspiration I have ever tapped". Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit", the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist" alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon. Flocon was delighted by Escher's "Grafiek

title: M. C. Escher in popular culture

text: to the artist. The film "Labyrinth" (1986) features a room based on the painting "Relativity". In the "Drawn Together" episode "Clara's Dirty Little Secret", Clara thinks she is pregnant, and Toot suggests that she fall down some stairs. Clara thinks of a suitable room and leads them to the "M. C. Escher room", where Toot pushes Clara down (and up, around, and back down) a flight of stairs. In the "Family Guy" episode "Brian Goes Back to College", Stewie and Brian share a room where Stewie puts up a framed print of "Relativity", which he calls "Crazy Stairs." He then

title: M. C. Escher in popular culture

text: The "Rick and Morty" episode "Morty's Mind Blowers" starts off with Rick and Morty running from a humanoid creature set in a place similar to Relativity. The "Futurama" episode "I, Roommate" features Relativity as one of the living spaces Fry and Bender are considering living in. M. C. Escher is alluded to in the Phineas and Ferb episode "Gaming the System" in which Candace Flynn is found in an environment similar to Relativity. In the city building game "Afterlife", Hell's ultimate punishment for Envy is called the Escher pit and is designed to torture souls by having them all be

title: M. C. Escher in popular culture

text: M. C. Escher in popular culture There are numerous references to famous Dutch painter M.C. Escher, in popular culture. The idea of Shahram Mokri's 2013 film "Fish & Cat" came from Escher's paintings. The director gives a change in the perspective of time in one single shot. In "" (2014), Sir Lancelot, Teddy Roosevelt, and Larry Daley enter the painting "Relativity", and experience the same strange gravity featured in the painting. In Dario Argento's "Suspiria" (1977), Escher's art is painted on several walls, as well as the main location of the film being on the fictitious "Escherstrasse", an obvious nod

title: M. C. Escher

text: shock": the infinite regular repetition of the tiles in the hyperbolic plane, growing rapidly smaller towards the edge of the circle, was precisely what he wanted to allow him to represent infinity on a two-dimensional plane. Escher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circles with which (he deduced) it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply. All the same, Escher persisted with hyperbolic tiling, which he called "Coxetering". Among the results were

title: M. C. Escher

text: stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Surinam and the Netherlands Antilles for the same commemoration. Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland. In 1937, the family moved again, to Uccle (Ukkel), a suburb of Brussels, Belgium. World War II forced them to move in January 1941, this time to Baarn, Netherlands, where Escher lived until 1970. Most of Escher's best-known works date from this period. The sometimes cloudy, cold, and wet weather of the Netherlands allowed

title: M. C. Escher

text: prints were mirror images of cones, spheres, cubes, rings, and spirals. Escher was also fascinated by mathematical objects such as the Möbius strip, which has only one surface. His wood engraving "Möbius Strip II" (1963) depicts a chain of ants marching forever over what, at any one place, are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. In Escher's own words: The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling artist in

title: Print Gallery (M. C. Escher)

text: in the void by treating the work as drawn on an elliptic curve over the field of complex numbers. They deem an idealized version of "Print Gallery" to contain a copy of itself (the Droste effect), rotated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58. Their website further explores the mathematical structure of the picture. "Print Gallery" has been discussed in relation to post-modernism by a number of writers, including Silvio Gaggi, Barbara Freedman, Stephen Bretzius, and Marie-Laure Ryan. Print Gallery (M. C. Escher) Print Gallery () is a lithograph printed in 1956 by the

title: Escher in the Palace

text: former Royal palace as an exhibition palace. Judd applied the principle of different colours and geometric patterns to the parquet floor in the Palace. Escher in the Palace Escher in Het Paleis ("Escher in The Palace") is a museum in The Hague, Netherlands, featuring the works of the Dutch graphical artist M. C. Escher. It is housed in the Lange Voorhout Palace since November 2002. In 2015 it was revealed that many of the prints on display at the museum were replicas, scanned from original prints and printed onto the same type of paper used by Escher, rather than original

title: Dragon (M. C. Escher)

text: the dragon's two-dimensional nature apparent. His head and neck pokes through one slit, and the tail through the other, with the head biting the tail in the manner of the ouroboros. In "Gödel, Escher, Bach", Douglas Hofstadter interprets the dragon's tail-bite as an image of self-reference, and his inability to become truly three-dimensional as a visual metaphor for a lack of transcendence, the inability to "jump out of the system". The same image has also been called out in the scientific literature as a warning about what can happen when one attempts to describe four-dimensional space-time using higher dimensions. A

title: Escher String Quartet

text: Escher String Quartet The Escher String Quartet is an American string quartet based in New York City, where they serve as Artists of the Chamber Music Society of Lincoln Center. Their name derives from the Dutch artist M. C. Escher. The Escher Quartet was founded in 2005 in New York City, where its original members were studying at the Manhattan School of Music. The group tours the US as well as internationally and has performed in Europe, Australia, and China. Among the venues where the ensemble has performed are the Auditorium du Louvre in Paris, Kennedy Center in Washington DC,

title: M. C. Escher

text: the series of wood engravings "Circle Limit I–IV". In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter". Escher's special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture. The Escher intellectual property is controlled by the M.C. Escher Company, while exhibitions of his artworks are managed separately by the M.C. Escher Foundation. The primary institutional collections of original works by M.C. Escher are the Escher Museum in The Hague; the National Gallery of Art (Washington, DC); the

title: George Arnold Escher

text: hydraulic engineer in Leeuwarden. In 1903 the family moved to Arnhem. George Arnold Escher George Arnold Escher (10 May 1843 – 14 June 1939) was a Dutch civil engineer and a foreign advisor to the Japanese government during the Meiji period. He was the father of the graphic artist M. C. Escher and the geologist Berend George Escher. Escher was hired by the Japanese government as a foreign advisor from September 1873 to July 1878, along with fellow Dutch civil engineers Johannis de Rijke and Cornelis Johannes van Doorn. During his stay in Japan, he designed and supervised the restoration

title: George Arnold Escher

text: George Arnold Escher George Arnold Escher (10 May 1843 – 14 June 1939) was a Dutch civil engineer and a foreign advisor to the Japanese government during the Meiji period. He was the father of the graphic artist M. C. Escher and the geologist Berend George Escher. Escher was hired by the Japanese government as a foreign advisor from September 1873 to July 1878, along with fellow Dutch civil engineers Johannis de Rijke and Cornelis Johannes van Doorn. During his stay in Japan, he designed and supervised the restoration of the Yodo river (Osaka), and built a harbour in Mikuni

title: M. C. Escher

text: him to focus intently on his work. After 1953, Escher lectured widely. A planned series of lectures in North America in 1962 was cancelled after an illness, and he stopped creating artworks for a time, but the illustrations and text for the lectures were later published as part of the book "Escher on Escher". He was awarded the Knighthood of the Order of Orange-Nassau in 1955; he was later made an Officer in 1967. In July 1969 he finished his last work, a large woodcut with threefold rotational symmetry called "Snakes", in which snakes wind through a pattern of linked

title: Escher in the Palace

text: Escher in the Palace Escher in Het Paleis ("Escher in The Palace") is a museum in The Hague, Netherlands, featuring the works of the Dutch graphical artist M. C. Escher. It is housed in the Lange Voorhout Palace since November 2002. In 2015 it was revealed that many of the prints on display at the museum were replicas, scanned from original prints and printed onto the same type of paper used by Escher, rather than original Escher prints as they had been labeled. The museum is housed in the Lange Voorhout Palace, a former royal residence dating back to the

title: M. C. Escher

text: the walls and ceilings, triggered his interest in the mathematics of tessellation and became a powerful influence on his work. Escher returned to Italy and lived in Rome from 1923 to 1935. While in Italy, Escher met Jetta Umiker – a Swiss woman, like himself attracted to Italy – whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons – Arthur and Jan. He travelled frequently, visiting (among other places) Viterbo in 1926, the Abruzzi in 1927 and

title: M. C. Escher

text: paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' continuously rising flights of steps, and enclosed a print of "Ascending and Descending" (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, "Waterfall" (1961). Escher was interested enough in Hieronymus Bosch's 1500 triptych "The Garden of Earthly Delights" to re-create part of its right-hand panel, "Hell", as a lithograph in 1935. He reused the figure of a Mediaeval woman in

title: M. C. Escher

text: he failed a number of subjects (due partly to a persistent skin infection) and switched to decorative arts, studying under the graphic artist Samuel Jessurun de Mesquita. In 1922, an important year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year, he traveled through Spain, visiting Madrid, Toledo, and Granada. He was impressed by the Italian countryside and, in Granada, by the Moorish architecture of the fourteenth-century Alhambra. The intricate decorative designs of the Alhambra, based on geometrical symmetries featuring interlocking repetitive patterns in the coloured tiles or sculpted into

title: M. C. Escher

text: Escher's work was held in Britain until 2015, when the Scottish National Gallery of Modern Art ran one in Edinburgh from June to September 2015, moving in October 2015 to the Dulwich Picture Gallery, London. The exhibition moved to Italy in 2015–2016, attracting over 500,000 visitors in Rome and Bologna, and then Milan. Doris Schattschneider identifies 11 strands of mathematical and scientific research anticipated or directly inspired by Escher. These are the classification of regular tilings using the edge relationships of tiles: two-color and two-motif tilings (counterchange symmetry or antisymmetry); color symmetry (in crystallography); metamorphosis or topological change; covering surfaces

title: Escher Cooperative House

text: Escher Cooperative House Escher Cooperative House, named after artist M. C. Escher, is one of the ICC's 19 student housing cooperatives. It is located at 1500 to 1520 Gilbert Court in Ann Arbor, Michigan. During the 1950s, the University of Michigan responded to post-war growth by developing North Campus, ensuring future demand for nearby student housing. The ICC persuaded the University to set aside three acres of a hilltop off Broadway for a "cooperative village." When the government made low-interest loans available in 1958, the ICC began planning in earnest. Due to University hesitation to co-sign, however, the project was

title: Escher Cooperative House

text: is expected to take three hours each week. Suite chores include vacuuming common areas, cleaning the suite kitchens, or serving as suite manager or on the house council (a group of suite elected people chosen to oversee house officers), and is expected to take around 30 minutes each week. The third division of labor is to clean hall bathrooms which is split between the members living in the 4 or 5 rooms bordering the bathroom. Escher Cooperative House Escher Cooperative House, named after artist M. C. Escher, is one of the ICC's 19 student housing cooperatives. It is located at

title: Three Worlds (Escher)

text: Three Worlds (Escher) Three Worlds is a lithograph print by the Dutch artist M. C. Escher first printed in December 1955. "Three Worlds" depicts a large pool or lake during the autumn or winter months, the title referring to the three visible perspectives in the picture: the surface of the water on which leaves float, the world above the surface, observable by the water's reflection of a forest, and the world below the surface, observable in the large fish swimming just below the water's surface. Escher also created a picture named "Two Worlds". The picture is based on true optical

title: M. C. Escher

text: en tekeningen" ("Graphics in Drawing"), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write the book "La Perspective curviligne" ("Curvilinear perspective"). Escher often incorporated three-dimensional objects such as the Platonic solids such as spheres, tetrahedrons, and cubes into his works, as well as mathematical objects such as cylinders and stellated polyhedra. In the print "Reptiles", he combined two- and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality: Escher's artwork is especially well-liked by mathematicians such as Doris Schattschneider and scientists such as Roger Penrose, who enjoy

title: M. C. Escher

text: as "The Drawbridge" in his "Carceri" ("Prisons") sequence depict perspectives of complex architecture with many stairs and ramps, peopled by walking figures. Only with 20th century movements such as Cubism, De Stijl, Dadaism, and Surrealism did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints. However, although Escher had much in common with, for example, Magritte's surrealism, he did not make contact with any of these movements. In his early years, Escher sketched landscapes and nature. He also sketched insects such as ants, bees, grasshoppers, and mantises, which appeared frequently in his later

title: M. C. Escher

text: Martin Gardner in his April 1966 Mathematical Games column in "Scientific American". Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums. He was one of the major inspirations of Douglas Hofstadter's Pulitzer Prize-winning 1979 book "Gödel, Escher, Bach". Maurits Cornelis Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of the civil engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved

title: Three Worlds (Escher)

text: effects, reflection and refraction. The angle of incidence is the line between the reflection of the trees and refraction allowing the view of the fish. Three Worlds (Escher) Three Worlds is a lithograph print by the Dutch artist M. C. Escher first printed in December 1955. "Three Worlds" depicts a large pool or lake during the autumn or winter months, the title referring to the three visible perspectives in the picture: the surface of the water on which leaves float, the world above the surface, observable by the water's reflection of a forest, and the world below the surface, observable

title: M. C. Escher

text: Italy (under Mussolini) became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear a Ballila uniform in school, the family left Italy and moved to Château-d'Œx, Switzerland, where they remained for two years. The Netherlands post office had Escher design a semi-postal stamp for the "Air Fund" in 1935, and again in 1949 he designed Netherlands

title: M. C. Escher

text: rings. These shrink to infinity toward both the center and the edge of a circle. It was exceptionally elaborate, being printed using three blocks, each rotated three times about the center of the image and precisely aligned to avoid gaps and overlaps, for a total of nine print operations for each finished print. The image encapsulates Escher's love of symmetry; of interlocking patterns; and, at the end of his life, of his approach to infinity. The care that Escher took in creating and printing this woodcut can be seen in a video recording. Escher moved to the Rosa Spier Huis

title: M. C. Escher

text: a two-pointed headdress and a long gown in his lithograph "Belvedere" in 1958; the image is, like many of his other "extraordinary invented places", peopled with "jesters, knaves, and contemplators". Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a "reality enthusiast"; he combined "formal astonishment with a vivid and idiosyncratic vision". Escher worked primarily in the media of lithographs and woodcuts, although the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures, and space. Integrated into his

title: M. C. Escher

text: transformed convex polygons into regular patterns in a plane to form a human motif. He extended the approach in his piece "Metamorphosis III", which is four metres long. In 1941 and 1942, Escher summarized his findings for his own artistic use in a sketchbook, which he labeled (following Haag) "Regelmatige vlakverdeling in asymmetrische congruente veelhoeken" ("Regular division of the plane with asymmetric congruent polygons"). The mathematician Doris Schattschneider unequivocally described this notebook as recording "a methodical investigation that can only be termed mathematical research." She defined the research questions he was following as Although Escher did not have mathematical training—his

title: M. C. Escher

text: with symmetric patterns; Escher's algorithm (for generating patterns using decorated squares); creating tile shapes; local versus global definitions of regularity; symmetry of a tiling induced by the symmetry of a tile; orderliness not induced by symmetry groups; the filling of the central void in Escher's lithograph "Print Gallery" by H. Lenstra and B. de Smit. The Pulitzer Prize-winning 1979 book "Gödel, Escher, Bach" by Douglas Hofstadter discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher's art and the music of J. S. Bach. The asteroid 4444 Escher was named

title: M. C. Escher

text: his use of polyhedra and geometric distortions. For example, in "Gravitation", animals climb around a stellated dodecahedron. The two towers of "Waterfall" impossible building are topped with compound polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron now known as Escher's solid. Escher had used this solid in his 1948 woodcut "Stars", which also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space. Escher possessed a 6 cm refracting telescope and was a keen-enough amateur astronomer

title: Stars (M. C. Escher)

text: aware of this reference and Coxeter writes that "It is remarkable that Escher, without any knowledge of algebra or analytic geometry, was able to rediscover this highly symmetrical figure." Martin Beech interprets the many polyhedral compounds within "Stars" as corresponding to double stars and triple star systems in astronomy. Beech writes that, for Escher, the mathematical orderliness of polyhedra depicts the "stability and timeless quality" of the heavens, and similarly Marianne L. Teuber writes that "Stars" "celebrates Escher's identification with Johannes Kepler's neo-Platonic belief in an underlying mathematical order in the universe". Alternatively, Howard W. Jaffe interprets the polyhedral forms

title: Stars (M. C. Escher)

text: octahedral compound of "Stars" in the beveled wire-frame style that had been used by Leonardo da Vinci in his illustrations for Luca Pacioli's 1509 book, "De divina proportione". The stella octangula (Latin for "eight-pointed star") in the upper right of "Stars" was first described by Pacioli, and later rediscovered by Kepler, who gave it its astronomical name. H. S. M. Coxeter reports that the shape of the central chameleon cage in "Stars" had previously been described in 1900 by Max Brückner, whose book "Vielecke und Vielflache" includes a photograph of a model of the same shape. However, Escher was not

title: Escher (programming language)

text: Escher (programming language) Escher (named for M. C. Escher, "a master of endless loops") is a declarative programming language that supports both functional programming and logic programming models, developed by J.W. Lloyd in the mid-1990s. It was designed mostly as a research and teaching vehicle. The basic view of programming exhibited by Escher and related languages is that a program is a representation of a theory in some logic framework, and the program's execution (computation) is a deduction from the theory. The logic framework for Escher is Alonzo Church's simple theory of types. Escher, notably, supports I/O through a monadic

title: Stars (M. C. Escher)

text: model heavenly bodies can be traced back to Plato, who in the "Timaeus" identified the regular dodecahedron with the shape of the heavens and its twelve faces with the constellations of the zodiac. Later, Johannes Kepler theorized that the distribution of distances of the planets from the sun could be explained by the shapes of the five Platonic solids, nested within each other. Escher kept a model of this system of nested polyhedra, and regularly depicted polyhedra in his artworks relating to astronomy and other worlds. Escher learned his wood engraving technique from Samuel Jessurun de Mesquita. He illustrated the

title: Stars (M. C. Escher)

text: polyhedral compounds float in the background; the four largest are, on the upper left, the compound of cube and octahedron; on the upper right, the stella octangula; on the lower left, a compound of two cubes; and on the lower right, a solid version of the same octahedron 3-compound. The smaller polyhedra visible within the print also include all of the five Platonic solids and the rhombic dodecahedron. In order to depict polyhedra accurately, Escher made models of them from cardboard. Two chameleons are contained within the cage-like shape of the central compound; Escher writes that they were chosen as

title: M. C. Escher

text: work. His early love of Roman and Italian landscapes and of nature created an interest in tessellation, which he called "Regular Division of the Plane"; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his artworks. He wrote, "Mathematicians have opened the gate leading to an extensive domain". After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations, Escher began to explore the

title: Another World (M. C. Escher)

text: the horn, however the horizontal view reverses the relative positions of the statue and the horn, and rotates the horn 180 degrees. The previous month (December 1946), Escher created a mezzotint called "Another World (Other World Gallery)". The image in that print is the same as this one except that the arches continue on as an infinite corridor. The bird/human sculpture is a real sculpture which was given to Escher by his father-in-law. This sculpture first appears in Escher's 1934 lithograph "Still Life with Spherical Mirror". The picture is featured in the cover of the 1965 edition of Italo Calvino's

title: Escher (programming language)

text: type representing the 'outside world', in the style of Haskell. One of the goals of Escher's designers was to support meta-programming, and so the language has comprehensive support for generating and transforming programs. Escher (programming language) Escher (named for M. C. Escher, "a master of endless loops") is a declarative programming language that supports both functional programming and logic programming models, developed by J.W. Lloyd in the mid-1990s. It was designed mostly as a research and teaching vehicle. The basic view of programming exhibited by Escher and related languages is that a program is a representation of a theory in

title: M. C. Escher

text: understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds that he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was "Still Life and Street" (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as "Relativity" (1953). "House of Stairs" (1951) attracted the interest of the mathematician Roger Penrose and his father, the biologist Lionel Penrose. In 1956, they published a

title: M. C. Escher

text: National Gallery of Canada (Ottawa); the Israel Museum (Jerusalem); and the Huis ten Bosch (Nagasaki, Japan). Despite wide popular interest, Escher was for a long time somewhat neglected in the art world; even in his native Netherlands, he was 70 before a retrospective exhibition was held. In the twenty-first century, major exhibitions have been held in cities across the world. An exhibition of his work in Rio de Janeiro attracted more than 573,000 visitors in 2011; its daily visitor count of 9,677 made it the most visited museum exhibition of the year, anywhere in the world. No major exhibition of

title: M. C. Escher in popular culture

text: breaks it while playing Ultimate Frisbee and asks "Oh no, did that hit crazy stairs?". In a later episode, "No Meals on Wheels", Peter complains that the fact that his new restaurant is attracting paraplegics "is weirder than that rap video by M.C. Escher." Escher is then depicted inside "Relativity" dressed like MC Hammer in "U Can't Touch This". and rapping, "Going up the stairs and going down the stairs and going up the stairs and going down the stairs and going up the sideways stairs." On the SyFy show "Warehouse 13", Escher is said by the character Leena to

title: Print Gallery (M. C. Escher)

text: without beginning or end." Escher attempted to do this with straight lines, but intuitively switched to using curved lines which make the grid expand greatly as it rotates. In the book "Gödel, Escher, Bach", Douglas Hofstadter explains it as a strange loop showing three kinds of "in-ness": the gallery is physically in the town ("inclusion"); the town is artistically in the picture ("depiction"); the picture is mentally in the person ("representation"). Escher's signature is on a circular void in the center of the work. In 2003, two Dutch mathematicians, Bart de Smit and Hendrik Lenstra, reported a way of filling

title: M. C. Escher

text: to Arnhem, where he attended primary and secondary school until 1918. Known to his friends and family as "Mauk", he was a sickly child and was placed in a special school at the age of seven; he failed the second grade. Although he excelled at drawing, his grades were generally poor. He took carpentry and piano lessons until he was thirteen years old. In 1918, he went to the Technical College of Delft. From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts. He briefly studied architecture, but

title: M. C. Escher

text: 1929, Corsica in 1928 and 1933, Calabria in 1930, the Amalfi coast in 1931 and 1934, and Gargano and Sicily in 1932 and 1935. The townscapes and landscapes of these places feature prominently in his artworks. In May and June 1936, Escher travelled back to Spain, revisiting the Alhambra and spending days at a time making detailed drawings of its mosaic patterns. It was here that he became fascinated, to the point of obsession, with tessellation, explaining: The sketches he made in the Alhambra formed a major source for his work from that time on. He also studied the architecture

title: Waterfall (M. C. Escher)

text: from the lower right, which means that from the viewer's perspective the two left-hand turns are directly in line with each other, while the waterwheel, the forward turn and the end of the aqueduct are all in line. The second left-hand turn is supported by pillars from the first, while the other two corners are supported by a tower of pillars that begins at the waterwheel. The water falls off the edge of the aqueduct and over the waterwheel in an impossible infinite cycle; in his notes on the picture, Escher points out that some water must be periodically added

title: M. C. Escher in popular culture

text: be one of the architects, along with Thomas Edison and Nikola Tesla, who designed the Warehouse. The Escher Vault's design resembles the lithograph "Relativity". Inside this vault, the stairwells and walls are constantly moving. Anyone not wearing specially designed glasses run the risk of being lost forever once inside. H.G. Wells is the only known individual to have successfully navigated the Escher Vault without glasses, instead using her Inperceptor Vest to retrieve personal items stored within. In the "Star vs. the Forces of Evil" episode "Interdimensional Field Trip", Janna, the classmate of Star falls in a construction similar to Relativity.

title: Rudolf George Escher

text: Rudolf George Escher Rudolf Escher (8 January 1912 in Amsterdam – 17 March 1980 in De Koog) was a Dutch composer and music theorist. He left compositions for chamber orchestra and orchestra, vocal and one electronic composition. Escher was also a poet, painter and writer. Escher was born the son of the geologist and mineralogist Berend George Escher and the Swiss Emma Brosy. His father was a son of the engineer George Arnold Escher and half-brother of the graphic artist Maurits Cornelis Escher. At the age of four, Escher moved with his family to Batavia, Dutch East Indies, where his

title: Berend George Escher

text: Berend George Escher Berend George Escher (April 4, 1885 in Gorinchem – October 11, 1967 in Arnhem) was a Dutch geologist. Escher had a broad interest, but his research was mainly on crystallography, mineralogy and volcanology. He was a pioneer in experimental geology. He was a half-brother of the artist M.C. Escher, and had some influence on his work due to his knowledge of crystallography. M.C. Escher created a woodcut ex libris for his brother Beer with a stylized image of a volcano around 1922 (Bool number 91). Escher was the son of G.A. Escher, a director of the Dutch

title: Roger Penrose

text: by Arne Bjerhammar in 1951. Having started research under the professor of geometry and astronomy, Sir W. V. D. Hodge, Penrose finished his PhD at Cambridge in 1958, with a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle in the 1950s, describing it as "impossibility in its purest form", and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. Escher's Waterfall, and Ascending and Descending were in turn inspired by Penrose. As reviewer Manjit Kumar puts it: Having become

title: Joust 2: Survival of the Fittest

text: portray a progression of villains, the staff added a new enemy, Knight Lord. The developers added backgrounds to the levels, inspired by artwork by M. C. Escher, Newcomer's favorite artist. Staff added a transform button to provide players with more variety and balance the gameplay. Williams shipped around 1,000 units of "Joust 2", significantly fewer than its predecessor. Brett Alan Weiss of Allgame and Mike Bevan of "Retro Gamer" attributed the poor numbers to an industry slump in the mid-1980s. "Joust 2" arcade cabinets have since become fairly rare among collectors. Weiss negatively compared the game to its predecessor, calling

title: Snakes (M. C. Escher)

text: The image is printed in three colours: green, brown and black. In several earlier works Escher explored the limits of infinitesimal size and infinite number, for example the "Circle Limit" series, by actually carrying through the rendering of smaller and smaller figures to the smallest possible sizes. By contrast, in "Snakes", the infinite diminution of size – and infinite increase in number – is only suggested in the finished work. Nevertheless, the print shows very clearly how this rendering would have been carried out to the limits of human visibility. This was Escher’s last print. Fredrik Ullén used this print

title: Relativity (M. C. Escher)

text: such as these can be found in many other Escher works. In the world of "Relativity", there are three sources of gravity, each being orthogonal to the two others. Each inhabitant lives in one of the gravity wells, where normal physical laws apply. There are sixteen characters, spread between each gravity source, six in one and five each in the other two. The apparent confusion of the lithograph print comes from the fact that the three gravity sources are depicted in the same space. The structure has seven stairways, and each stairway can be used by people who belong to

title: Stars (M. C. Escher)

text: (1947). Escher's later work "Four Regular Solids (Stereometric Figure)" returned to the theme of polyhedral compounds, depicting a more explicitly Keplerian form in which the compound of the cube and octahedron is nested within the compound of the dodecahedron and icosahedron. "Stars" was used as cover art for the 1962 anthology "Best Fantasy Stories" edited by Brian Aldiss, and for a 1971 Italian edition of occult guidebook "The Morning of the Magicians". It also formed the frontispiece for a 1996 textbook on crystallography. As well as being exhibited in the Escher Museum, copies of "Stars" are in the permanent collections

title: Stars (M. C. Escher)

text: was produced by carving the artwork into the end grain of a block of wood (unlike a woodcut which uses the side grain), and then using this block to print the image. It was created by Escher in October 1948. Although most published copies of "Stars" are monochromatic, with white artwork against a black background, the copy in the National Gallery of Canada is tinted in different shades of turquoise, yellow, green, and pale pink. The print depicts a hollowed-out compound of three octahedra, a polyhedral compound composed of three interlocking regular octahedra, floating in space. Numerous other polyhedra and

title: Become What You Are

text: more universal. The title of the album was inspired by German philosopher Friedrich Nietzsche, whom Hatfield admired. The album was recorded at Hollywood Sound, mixed at Oceanway Studios and mastered at Precision Mastering in Los Angeles. It was released on August 3, 1993, by Mammoth Records. The song "Spin the Bottle" is featured on the soundtrack of the 1994 film "Reality Bites". As of February 2010, "Become What You Are" had sold 267,000 copies in the US according to Nielsen SoundScan. "Become What You Are" received generally favorable reviews. Stephen Thomas Erlewine of AllMusic praised Hatfield's honest vocals on "Supermodel,"

title: Stars (M. C. Escher)

text: Stars", completed in August 1948, depicts wireframe versions of several of the same polyhedra and polyhedral compounds, floating in black within a square composition, but without the chameleons. The largest polyhedron shown in "Study for Stars", a stellated rhombic dodecahedron, is also one of two polyhedra depicted prominently in Escher's 1961 print "Waterfall". The stella octangula, a compound of two tetrahedra that appears in the upper right of "Stars", also forms the central shape of another of Escher's astronomical works, "Double Planetoid" (1949). The compound of cube and octahedron in the upper left was used earlier by Escher, in "Crystal"

title: Stars (M. C. Escher)

text: in "Stars" crystallographically, as "brilliantly faceted jewels" floating through space, with its compound polyhedra representing crystal twinning. However, R. A. Dunlap points out the contrast between the order of the polyhedral forms and the more chaotic biological nature of the chameleons inhabiting them. In the same vein, Beech observes that the stars themselves convey tension between order and chaos: despite their symmetric shapes, the stars are scattered apparently at random, and vary haphazardly from each other. As Escher himself wrote about the central chameleon cage, "I shouldn't be surprised if it wobbles a bit." A closely related woodcut, "Study for

title: Alfred Escher

text: the "Neuberg" on Hirschengraben in Zürich. Heinrich Escher had a country house built on the left shore of Lake Zürich in the village of Enge (now part of the city of Zürich). He called it "Belvoir". When the family moved into the house in 1831, Heinrich Escher was able to devote himself fully to his passion for botany and his entomological collection. During this period Alfred Escher was taught at home by various tutors, including the theologian Alexander Schweizer, and Oswald Heer, who was to become a paleo-botanist and entomologist. Escher attended the Zürich Obergymnasium high school from 1835 to

title: M. C. Escher in popular culture

text: given different punishments, and after a few days are allowed to switch with a neighbor, thinking he/she is better off, only to find that all punishments are worse than the last. The outside slightly resembles Relativity. In "AdventureQuest Worlds", the first lord of chaos is Escherion, who has the ability to invert objects and lives in a castle with an inside similar to "Relativity". In the Psygnosis game "Lemmings", the 18th level of "Taxing" is named "Tribute to M.C. Escher", as the solution involves building a zigzag stairway slightly reminiscent of "Relativity". During the last decades several video games have

title: Mathematics and art

text: Isaac Newton's work on the optical spectrum influenced Goethe's "Theory of Colours" and in turn artists such as Philipp Otto Runge, J. M. W. Turner, the Pre-Raphaelites and Wassily Kandinsky. Artists may also choose to analyse the symmetry of a scene. Tools may be applied by mathematicians who are exploring art, or artists inspired by mathematics, such as M. C. Escher (inspired by H. S. M. Coxeter) and the architect Frank Gehry, who more tenuously argued that computer aided design enabled him to express himself in a wholly new way. The artist Richard Wright argues that mathematical objects that can