Abstract:
A game using tokens bearing a number (N&gt;2) of N-valued attributes, by finding, among tokens in each player&#39;s possession alone or in combination with those on a common playing field, groups of N tokens whose attributes, suitably permuted, form lines spanning the N-dimensional cube of N N  combinations, and to arrange the playing field to consist entirely of such groups and networks thereof.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/207,916, filed Feb. 18, 2009, which is incorporated by reference herein. 
     
    
     BACKGROUND 
       [0002]    The present invention relates to a game played by arranging tokens in patterns on a playing field according to rules that pertain to the tokens&#39; attributes. 
         [0003]    A well-known example of a game arranging token in patterns on a playing field is dominoes, which is played using a set of tokens called tiles or simply dominoes. Each domino is a block marked with two groups of zero to six dots or “pips” on one surface. Under the basic rules, at each turn, a player attempts to place the end of a domino from his or her hand beside another domino with an end that has a matching number of dots. All the dominoes on the playing field must be connected together. Pips at the ends of lines of tiles are counted with each turn to keep score in some variants of the game, which ends when some team or player has amassed a specified number of points. The public domain describes many details and rules for different games for those interested. More information on dominoes is available at various websites, including http://www.dominorules.com/domino basics.aspx. 
         [0004]    Popular as it is, the game of dominoes has some disadvantages. For example, it may become clear that one player&#39;s lead is insurmountable well before the end of the game, and kids (among others) may not want to continue a game they are sure to lose. The game of dominoes calls for little or no imaginative or radical problem-solving, in that it prohibits rearrangement of the dominoes after placement on the playing field. 
       SUMMARY OF THE INVENTION 
       [0005]    We recognized and addressed a need for a new game that rewards strategy over chance, can be played in a short time (e.g., a coffee break), holds winning in suspense until the end, and can be easily learned yet challenges players at many different levels. 
         [0006]    The present invention is a game played with a set of tokens (e.g., playing tiles) distinguishable by combinations of three or more attributes (i.e., characteristics of interest), each attribute having, on a given token, one of three or more discrete values. The game challenges players to shed all from their hands by (a) identifying playable groups of tokens—groups within which every attribute either (i) retains a single value or (ii) takes on each of its available values—and (b) constructing on a playing field an evolving pattern of tokens, in which (i) every continuous row or column of tokens consists of at least one playable group and (ii) every token belongs to at least one such continuous row or column. 
         [0007]    The game is designed for brief and spontaneous play, combining the challenge of recognizing special groups of tokens—among which the several attributes vary maximally or not at all—with the fun of arranging and linking such collections of tokens on a tabletop. Despite the apparent simplicity of its rules, the game rewards subtle reasoning and requires supple visualization. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
           [0009]      FIG. 1  illustrates a first embodiment including instructions, a typical playing tile in perspective view, and a plan view of twenty-seven tiles suitable for use as tokens. 
           [0010]      FIG. 2A  illustrates some examples of playable groups (in this case, triads) of tiles. 
           [0011]      FIG. 2B  illustrates examples of non-playable groups (not triads) of tiles. 
           [0012]      FIG. 3  is a flowchart to illustrate the sequences of steps used in playing the game. 
           [0013]      FIG. 4  is a tabular view of Player A and Player B initially drawing four tiles in a first play-by-play example of the game. 
           [0014]      FIG. 5  is a tabular view of a typical lottery to select the player who will start the game. 
           [0015]      FIG. 6  is a diagram that illustrates a game opening in which neither Player A nor Player B can build a triad and each must draw a fifth tile in turns  1  and  2 . 
           [0016]      FIG. 7  is a diagram that illustrates each player building one triad in turns  3  and  4 . 
           [0017]      FIG. 8  is a diagram that illustrates Player A building a triad and shedding one tile in turn  5 , and Player B drawing a tile in turn  6 . 
           [0018]      FIG. 9  is a diagram that illustrates Player A drawing a tile in turn  7 , and Player B building a triad and shedding two tiles in turn  8 . 
           [0019]      FIG. 10  is a diagram that illustrates Player A winning by shedding his last tiles in turn  9 . 
           [0020]      FIG. 11  is a diagram that illustrates turns  7  and  8  of an alternate ending, serving as a second play-by-play example, where Player A and Player B have agreed to reveal their tiles and, seeing the tile that Player A has drawn in turn  7 , Player B chooses to draw a tile in turn  8  rather than let Player A win as illustrated in  FIG. 10 . 
           [0021]      FIG. 12  is a diagram that illustrates Player A in turn  9  drawing a tile, and Player B in turn  10  completing a square perimeter. 
           [0022]      FIG. 13  is a diagram that illustrates Player A in turn  11  drawing a tile by default, and Player B in turn  12  drawing the unique tile that is capable of completing the square. 
           [0023]      FIG. 14  is a diagram that illustrates Player A in turn  13  playing a triad as a new island, and Player B starting turn  14  by filling in the square that was framed in turn  10 . 
           [0024]      FIG. 15  is a diagram that illustrates Player B continuing with turn  14  by trisecting the square into islands and linking the island built in turn  13  to one of the three new islands. 
           [0025]      FIG. 16  is a diagram that illustrates Player B finishing turn  14  by shedding the tiles withheld in turn  8 , and winning the game by virtue of strategy informed by revealed tiles. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0026]    A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
         [0027]    The following description includes the best mode of carrying out the invention. This detailed description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is determined by reference to the claims. 
         [0028]    The tiles in a first embodiment constitute a set of tokens distinguished by three attributes, each attribute ranging over three values, such that one tile bears each combination of available values of the attributes. 
         [0029]      FIG. 1  illustrates the first embodiment of the game, which includes, in addition to an opaque grab bag (not shown), twenty-seven solid tiles (tile  111  through tile  333 , with tile  111  shown in both perspective and plan views and the rest in plan view only), and instructions  20 . In this first embodiment, each tile bears a marking in one of three shapes (moon, sun, or star) rendered in one of three foreground colors (red, yellow or blue) on one of three background colors (green, violet or orange). 
         [0030]    Certain embodiments include rules that permit players to conceal the tokens that they hold. Any of several mechanisms can be used. For example, in the first embodiment the tiles (e.g. tile  111 ) are constructed with a thickness suitable for standing on edge, and of materials capable of concealing all indicia when viewed from behind (as by opposing players). Other embodiments may include a rack to hold each player&#39;s tiles at an angle that facilitates viewing by that player alone. 
         [0031]    In the first embodiment, the term “triad” is defined as any group of three tiles in which each attribute (i.e. foreground color, background color, or shape) either retains the same value or takes on all three available values. Thus, taking the shape attribute as an example, in a valid triad, either all three tiles bear the same shape (e.g., all three shapes are moons), or all three tiles bear different shapes (i.e., one moon, one star, and one sun). Similar conditions apply, independently, to the other two attributes. 
         [0032]    Players begin the game by drawing the minimum number of tokens (four) that can include a triad without constituting one (which would end the game). With each turn, a player either sheds some tiles from his or her hand by arranging one or more triad(s) on the playing field, or adds a randomly-drawn tile to his or her hand. 
         [0033]      FIG. 1  illustrates example instructions  20 , including the definition of a triad and the rules, for the first embodiment. The rules are substantially as follows:
   1. (a) Players agree to reveal or conceal tiles, then each player draws four tiles;
       (b) The one with the most red-marked shapes must take his or her turn first;   (c) The first player to run out of tiles will win the game.   
       2. During each turn, a player must either (a) shed one or more tile(s) by building triads on the playing field, or (b) draw a tile from the grab bag.   3. Players may freely rearrange triads already on the playing field, provided
       (a) every continuous row or column of tiles is a single triad, and   (b) every tile is in some triad disposed as a continuous row or column.   
         
         [0041]    The game appeals to, and aims to stimulate and challenge, the faculty of visualization, so color plays a natural role in certain embodiments. For example, in the first embodiment, the first two attributes of a tile are foreground and background colors. 
         [0042]    The tiles shown in  FIG. 1  are assigned three-digit reference numbers. The first digit signifies a foreground color: red (1xx) yellow (2xx) or blue (3xx). The second digit signifies a background color: green (x1x), violet (x2x) or orange (x3x). The third digit signifies a shape: a sun (xx1), a moon (xx2) or a star (xx3). For example, tile  111  is a red-on-green sun, tile  123  is a red-on-violet star, tile  222  is a yellow-on-violet moon and tile  333  is a blue-on-orange star. In alternative embodiments, any three colors (including shades of gray) can be used for the foreground color and any other three colors can be used for the background. 
         [0043]    The three-digit reference numbers in the drawings refer to the tiles as follows: 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 111: red-on-green sun 
                 112: red-on-green moon 
                 113: red-on-green star 
               
               
                 121: red-on-violet sun 
                 122: red-on-violet moon 
                 123: red-on-violet star 
               
               
                 131: red-on-orange sun 
                 132: red-on-orange moon 
                 133: red-on-orange star 
               
               
                 211: yellow-on-green sun 
                 212: yellow-on-green moon 
                 213: yellow-on-green star 
               
               
                 221: yellow-on-violet sun 
                 222: yellow-on-violet moon 
                 223: yellow-on-violet star 
               
               
                 231: yellow-on-orange sun 
                 232: yellow-on-orange moon 
                 233: yellow-on-orange star 
               
               
                 311: blue-on-green sun 
                 312: blue-on-green moon 
                 313: blue-on-green star 
               
               
                 321: blue-on-violet sun 
                 322: blue-on-violet moon 
                 323: blue-on-violet star 
               
               
                 331: blue-on-orange sun 
                 332: blue-on-orange moon 
                 333: blue-on-orange star 
               
               
                   
               
             
          
         
       
     
         [0044]      FIG. 2A  illustrates a triad  22  in which none of the attributes varies. This can occur in embodiments comprising three complete sets of the twenty-seven tiles shown in the table above.  FIG. 2A  also illustrates a triad  24  in which one attribute varies (maximally, as it must if it varies at all) among the three tiles, a triad  26  in which two attributes vary, and a triad  28  in which all three attributes vary among the three tiles. 
         [0045]      FIG. 2B  illustrates several examples of groups of tiles that do not constitute triads. Group  30  is not a triad because an attribute varies incompletely, in that the three tiles have just two foreground colors. Group  32  is not a triad because it has incomplete variation in background color. Group  33  is not a triad because it has incomplete variation in shape. Groups  34  and  36  are not triads because each contains more or less than three tiles. 
         [0046]      FIG. 3  is a flowchart illustrating the steps of playing the game. At step  40 , the players determine whether the tiles will be revealed or concealed, and each player draws four tiles from a grab bag.  FIG. 4  illustrates two players drawing their initial hands (i.e., the collections of tiles in their possession): Player A draws hand  70 , consisting of tiles  121 ,  132 ,  311  and  322 , and Player B draws hand  72  consisting of tiles  112 ,  323 ,  113  and  212 . The playing field  74  is initially empty. 
         [0047]      FIG. 3 , in steps  42 ,  44 ,  46 ,  48 ,  49  and  50 , illustrates a method to select the player who will start the game, based on the number of tiles each player holds with a particular attribute value. In the first embodiment, we compare the numbers of tiles bearing a red foreground color. When the players have agreed to reveal tiles at step  40 , the “No” branch is taken from decision step  42  to decision step  46 , where all the players can see whether some player&#39;s initial hand has more red-marked tiles than the other hands or there is a tie. If there is a tie, then every tied player temporarily draws another tile and reveals it at step  48 . This lottery proceeds, looping back to decision step  46 , until the tie is broken and the “No” branch is taken. When the players have agreed to conceal tiles, the “Yes” branch is taken from decision step  42  and the loop of steps  46  and  48  is preceded by each player temporarily drawing a tile and revealing it at step  44  to determine the starting player. At step  49 , any tiles drawn to break a tie are returned to the grab bag. At step  50 , the player who showed the greatest number of red-marked tiles is designated the starting player.  FIG. 5  is a table representing a possible course of this lottery to determine which player will take the first turn. As shown in tabular form, player A breaks the tie by drawing the red-on-violet star  123 , and will have the first turn. 
         [0048]    One turn consists of the player&#39;s attempt to shed tiles while arranging the playing field to consistent entirely of triads in accordance with rule  3  described earlier. At decision step  52 , the player determines if he or she can shed any tile(s). If the player can shed and chooses to shed, following the “Yes” branch of  52  and the “Yes” branch of  54 , the player sheds tile(s) at step  56 . If this leaves any tiles in the player&#39;s hand, taking the “Yes” branch of decision step  58 , the player passes the grab bag to the next player at step  62 . If the player shed the last tile, the player wins the game at step  64 . 
         [0049]    At step  62 , the player signals completion of his or her turn. This is necessary because the player may rearrange the tiles on the playing field in several steps, any one of which would have satisfied rule  3 , as shown in  FIGS. 14-16 . So, returning to  FIG. 3 , if the player is left with any tiles (the “Yes” branch of decision step  58 ), he or she signals completion of the turn by passing the grab bag to the next player at step  62  (or at least touching the grab bag). Interrupting the player&#39;s turn by drawing a tile is its own punishment, but trying to shed a tile before the player signals completion of the turn may be discouraged by forcing the interrupting player to draw another tile. 
         [0050]    If the player does not shed at least one tile at step  56 , whether by choice as in the “No” branch of decision step  54  or by inability as in the “No” branch of decision step  52 , he or she must draw one tile from the grab bag in step  60 , concluding the player&#39;s turn. 
         [0000]    Play-by-Play Account of an Example Game with Tiles Concealed by Default 
         [0051]    Recapitulating the opening of the example game, we assume that the players have not agreed to reveal tiles ( FIG. 3 , step  42 ), and are therefore concealing their tiles from one another. Players A and B draw hands  70  and  72  ( FIG. 4 ). We also assume that Player A is the first to take a turn, by lottery as previously described ( FIG. 5 ). As shown in  FIG. 6 , Player A, having no triads in her hand, draws tile  231  in turn  1 . Player B, having no triads in his hand, draws tile  111  in turn  2 . The playing field remains empty. 
         [0052]    Tiles newly drawn or shed by either player are shown with heavier borders. Also, in actual play, rows or columns of tiles would be more closely spaced than they appear in the game examples. They are shown with some separation to emphasize their mobility, and for clearer demarcation of groups of tiles such as item  90  in  FIG. 12 . 
         [0053]      FIG. 7  illustrates a case in which the players shed tiles by building triads. In turn  3 , Player A sheds tiles  121 ,  311  and  231  by building triad  80 . In turn  4 , Player B sheds tiles  112 ,  113  and  111  by building triad  82 . 
         [0054]      FIG. 8  illustrates rearrangement of tiles on the playing field to shed a tile. In turn  5 , Player A rearranges the tiles of triads  80  and  82  to align tile  231  with tile  113 , and sheds tile  322  to link them. The rearranged triads,  84  and  86 , are no longer islands, but linked by a triad made of tiles  113 ,  322  and  231 . The corner tiles  113  and  231  are not available for additional connections due to rule  3 ( a ) prohibiting continuous lines of more than three tiles. However, if the linking tile  322  is later moved for use elsewhere on the playing field, the tiles  113  and  231  will be freed as well. This is an advantage to the game as one can freely arrange the tiles on the playing field as long as rule  3  is satisfied.  FIG. 8  also shows turn  6 , in which Player B sees no opportunity to build a triad and draws tile  312 . He can use tile  312  to form a triad, but not until his next turn. 
         [0055]    In  FIG. 9 , turn  7 , Player A draws tile  222 , observing that the playing field has not changed since her last move. In turn  8 , Player B builds the triad  88  downward from triad  86  ( FIG. 8 ), shedding his tile  212  and the recently-drawn tile  312 . However, if the players had agreed to reveal tiles in their respective hands, Player B might opt to draw another tile from the grab bag rather than put tile  312  on the playing field, which would seal his fate for the following reason: Player A holds tile  132  and tile  222 , which like any pair of tiles uniquely determine which tile would complete a triad. In this case, tile  312  is the very tile Player A needs to have available on the playing field in order to shed her last two tiles. 
         [0056]    Player B is unaware of that problem, because the tiles of Player A are concealed by agreement.  FIG. 10 , turn  9 , illustrates the outcome: Player A aligns her tiles  132  and  222  with the tile  312  just played by Player B, emptying her hand and winning the game. 
         [0000]    Play-by-Play Account of an Example Game with Tiles Revealed by Agreement 
         [0057]    The players in the foregoing game had the option of agreeing in advance to reveal, rather than conceal, their tiles. Supposing this to have been their mutual choice, the game might have ended differently, with strategy playing a stronger role. 
         [0058]      FIG. 11  illustrates how turns  7  and  8  might have gone, supposing the same tiles had been drawn and the same moves had been made through turn  6 . Player B could have seen that shedding his tile  312  would enable Player A to win. In order to preserve a chance of winning, Player B might have opted to draw another tile from the grab bag at turn  7  rather than provide tile  312  to Player A. Suppose the tile that Player B draws, to avert defeat, is tile  131  (Player A&#39;s snarky remarks on the stinginess not shown). 
         [0059]    In  FIG. 12 , Player A next draws a tile  331  in turn  9 . Player B rearranges triad  84  ( FIG. 11 ) into triad  90 , then sheds tile  131 , closing a square of four triads  92  in turn  10 . 
         [0060]      FIG. 13 , turns  11  and  12 , illustrate another case where Players A and B cannot see how to build one or more triad(s) and both must draw tiles. They draw tiles  233  and  213 , respectively. If Player A doesn&#39;t stop him, Player B can use tile  213  in his next turn to transform the square of four triads  92  into a solid three-by-three square of triads. 
         [0061]      FIG. 14 , turn  13 , has Player A shedding tile  132 , tile  331 , and tile  233  to build an isolated triad  94 . Turn  14  begins with Player B filling in the square of triads  95  with the tile  213  drawn in his previous turn. This move illustrates one remarkable result of rule  3 : the unique tile that completes the middle row of any given square perimeter of triads is always the same tile that completes the middle column of that square perimeter. 
         [0062]      FIG. 15  illustrates that a player who completes a solid square creates multiple possibilities for the former corner tiles to form new connections. Turn  14  continues with Player B separating the square of triads  95  ( FIG. 14 ) into three triads  96 ,  98  and  99 , and shedding tile  323  to link the former corner tile  113  to tile  233 . 
         [0063]    In  FIG. 16 , turn  14  ends with Player B shedding tiles  212  and  312  by combining them with tile  112  to form a triad, emptying his hand, and winning the game. 
       Some Consequences of the Rules of the Preferred Embodiment 
       [0064]    Rule  3  permits tiles to be built on the playing field in “islands” (isolated triads) such as triad  80  and triad  82  shown in  FIG. 7 , in chains as shown in  FIG. 11 , in networks as shown in  FIG. 9 , in 3×3 square perimeters such as triad  92  in  FIG. 12 , or in solid 3×3 squares such as triad  95  in  FIG. 14 , and in some other configurations combining these. 
         [0065]    As an unexpected result of Rule  3 , illustrated in  FIG. 14  and noted above, when eight tiles form a square perimeter of four triads (each corner tile belonging to two triads), the single tile that would be required in order to complete a triad with the middle tiles in any two opposite sides of this square is always identical with the tile that would complete a triad joining the middle tiles of the other two sides, whence such an empty square can always be filled in by some particular tile. (Diagonals of such a square do not generally form triads, and they don&#39;t have to, because rule  3 ( a ) only requires continuous rows or columns of tokens to consist of triads.) The resulting solid square can be trisected, that is, sliced into three triads, either horizontally or vertically, presenting various possibilities for former corner tiles to make new connections. Since the opposing player(s) will have similar possibilities at their disposal, such a move may be best reserved for the last turn. 
       Certain Alternative Embodiments 
       [0066]    The above embodiment is one of a family of games within the ambit of the invention, each game using a set of tiles or tokens bearing a number (N&gt;2) of N-valued attributes. The number of distinct tokens needed to cover all the combinations is (number of values) raised to the power (number of attributes), or N N , hence the number of tokens is at least 3 3 =27. For a given value of N, a “playable group” is defined as a group of N tokens in which each attribute either retains a single value or takes on all N allowed values. With this general notion of a “playable group” (which includes a “triad”), the generalized rules become:
   1. (a) Players agree to reveal or conceal tiles, then each player draws N+1 tiles;
       (b) The starting player is selected by lottery or by agreement;   (c) The first player to run out of tokens will win the game.   
       2. During each of their turns, players must either:
       (a) use up some of their own tokens by building playable groups on the table, or   (b) draw a token at random from the grab bag.   
       3. Players may freely rearrange playable groups already on the table, provided
       (a) every continuous row or column of two or more tokens consists of a playable group; and   (b) every token is in some playable group disposed as a continuous row or column.   
       
 
         [0076]    With the number of attributes (and of values) N=4, there would be 4 4 =256 tokens, corresponding directly to bytes. This variant of the rules would be especially amenable to embodiment in a computing device. The attributes in this case would be fields of two bits within a byte, each bit field admitting of 4 values. Larger values of N are also conceivable although it would entail at least 5 5 =3,125 tokens. 
         [0077]    The choice of attributes for the tokens is arbitrary, to such an extent that the tokens themselves, as well as the playing field and the hands of one or more players, may in some embodiments appear only as images displayed by one or more computing devices. The game-playing apparatus embodying the invention in such cases would consist of a computing device including a processor executing a program designed to supervise the execution of externally-supplied software algorithms and to verify their conformance to the rules disclosed here. The supervisory program would enable such software algorithms to play against one another, in addition to or instead of one or more humans. In several embodiments, the software is implemented on a computing device such as a PC, an Apple computer, an Apple iPhone, or a Web application. 
         [0078]    Thus the game-playing apparatus may comprise a computing device programmed to execute competing game-playing algorithms or accept commands from competing agents. The playing field and players&#39; hands would exist in the memory of the computing device and could also be depicted in a computer display. Play would be controlled by (i) one or more human players, or (ii) one or more instances of competing algorithms programs, or (iii) agents of both types. 
         [0079]    Other embodiments of the game, suitable for more than four players, are readily derived by combining multiple sets of tokens. 
         [0080]    The first embodiment includes an opaque grab bag of suitable size and design (not shown) to store all the tiles, mix them up, and manually remove them individually during a game. Such a grab bag, while not essential to the invention, is an element of that embodiment because it serves both as a way to identify the current player and as a convenient package for the tiles. Any suitable shuffling or randomizing dispenser could substitute for the grab bag. 
         [0081]    The instructions  20  in  FIG. 1 , taking a geometrical approach to explain the concept of a triad, indicate that the tiles could be arranged by their attributes to form a 3×3×3 block or “cube.” For example, one could construct the cube by stacking or layering the 3×3 square of nine tiles (x1x) with a green background atop the nine tiles (x2x) with a purple background, which are stacked atop the nine tiles (x3x) with an orange background. The instructions  20  define a “triad” as a set of three tiles that would form a straight line in any direction, even diagonally, through such a “cube” of attributes. In some alternative embodiments, rules may prohibit space diagonals and/or plane diagonals. Prohibiting space diagonals would mean that at least one attribute would have to be held constant; prohibiting plane diagonals as well would mean that only one attribute could vary (maximally, if at all) in a valid triad. 
         [0082]    Rule  3 ( a ) effectively limits the number of playable groups that can share a given token to two. We have found that requiring every continuous row or column of tokens to be a single playable group does not unduly limit possible moves so much as it forces us to search more deeply for available moves than if playable groups could extend in all four directions from one tile. However, in some embodiments, the rule may be dropped, so that a tile can belong to up to four playable groups. Even in such cases, every continuous row or column of two or more tokens must consist of one or more playable groups. 
         [0083]    All three (or N) attributes may be freely chosen, while preserving the challenge of constructing networks of playable groups of tokens on a playing field. For example, the length, width and depth of the token could be used as attributes, or the shape of the token itself, its surface texture, and its consistency could form an alternative, tactile attribute space. The attribute of shape need not be used, but if it is, numerous alternatives exist, such as squares, circles and triangles, or depictions of planes, trains and automobiles. In other embodiments, background color could be replaced by other attributes such as number of markings as described in U.S. Provisional Application No. 61/207,916, or surface finish (e.g. glossy, matte, rough) or material (e.g. wood, metal, stone).