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can be generated by tiles in the form of a white square with a black diagonal. As with the quarter-circle tiles, each such tile has two orientations. The connectivity of the resulting labyrinth can be analyzed mathematically using
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of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling.
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The tile originally studied by
Truchet is split along the diagonal into two triangles of contrasting colors. The tile has four possible orientations.
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275:(1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy",
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Inverse of the
Truchet tile, created by any 90° rotation or orthogonal flip
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as bond percolation at the critical point of a diagonally-oriented grid.
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entitled "Mémoire sur les combinaisons", and were popularized in 1987 by
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This type of tile has also been used in abstract strategy games
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302:. With a translation of Truchet's text by Pauline Boucher.
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Browne, Cameron (2008), "Truchet curves and surfaces",
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Truchet tiles were first described in a 1704 memoir by
28:
are square tiles decorated with patterns that are not
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Some examples of surface filling made tiling such a
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102:A second common form of the Truchet tiles, due to
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8:
318:10 PRINT CHR$ (205.5+RND(1)); : GOTO 10
187:10 PRINT CHR$ (205.5+RND(1)); : GOTO 10
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701:Dividing a square into similar rectangles
200:A labyrinth generated from diagonal tiles
362:The Truchet Tiles and the Diamond Puzzle
232:
310:
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185:required to generate such patterns -
103:
7:
356:https://truchetpatterns.netlify.app/
354:Online Truchet Pattern Generator:
14:
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493:
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1:
726:Regular Division of the Plane
178:considers the single line of
634:Architectonic and catoptric
532:Aperiodic set of prototiles
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259:10.1016/j.cag.2007.10.001
157:, prior to Smith's work.
18:information visualization
247:Computers & Graphics
315:Montfort, Nick (2012).
139:We have such a tiling:
87:With random placement:
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30:rotationally symmetric
199:
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93:
83:
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56:Contrasting triangles
273:Smith, Cyril Stanley
45:Cyril Stanley Smith
32:. When placed in a
338:Weisstein, Eric W.
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172:percolation theory
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68:
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646:Computer graphics
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193:, a found poem".
41:Sébastien Truchet
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713:Conway criterion
640:Circle Limit III
611:
544:Einstein problem
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433:Schwarz triangle
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341:"Truchet Tiling"
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120:The Truchet tile
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476:Wallpaper group
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360:Ibáñez, Raúl, "
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291:10.2307/1578535
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216:Wallpaper group
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155:Black Path Game
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98:Quarter-circles
77:With a scheme:
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330:External links
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285:(4): 373–385,
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253:(2): 268–281,
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22:graphic design
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191:concrete poem
184:
181:
177:
176:Nick Montfort
173:
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88:
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61:
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50:
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42:
37:
35:
34:square tiling
31:
27:
26:Truchet tiles
23:
19:
1470:Tessellation
737:Substitution
732:Regular grid
724:
638:
596:
571:Quaquaversal
469:Kisrhombille
399:Tessellation
344:
321:. MIT Press.
317:
282:
276:
267:
250:
246:
180:Commodore 64
164:
148:
138:
104:Smith (1987)
101:
86:
76:
69:
59:
38:
25:
15:
767:vertex type
625:Anisohedral
580:Self-tiling
423:Pythagorean
211:Girih tiles
189:- to be "a
1464:Categories
671:Pentagonal
227:References
221:Wang tiles
51:Variations
779:Spherical
747:Voderberg
708:Prototile
675:Problems
651:Honeycomb
629:Isohedral
516:Aperiodic
454:honeycomb
438:Rectangle
428:Rhombille
346:MathWorld
167:labyrinth
1475:Patterns
861:V3.4.3.4
696:Squaring
691:Heesch's
656:Isotoxal
576:Rep-tile
566:Pinwheel
459:Coloring
412:Periodic
278:Leonardo
205:See also
161:Diagonal
153:and the
1321:6.4.8.4
1276:5.4.6.4
1236:4.12.16
1226:4.10.12
1196:V4.8.10
1171:V4.6.16
1161:V4.6.14
1061:3.6.4.6
1056:3.4.∞.4
1051:3.4.8.4
1046:3.4.7.4
1041:3.4.6.4
991:3.∞.3.∞
986:3.4.3.4
981:3.8.3.8
976:3.7.3.7
971:3.6.3.8
966:3.6.3.6
961:3.5.3.6
956:3.5.3.5
951:3.4.3.∞
946:3.4.3.8
941:3.4.3.7
936:3.4.3.6
931:3.4.3.5
886:3.4.6.4
856:3.4.3.4
849:regular
816:Regular
742:Voronoi
666:Packing
597:Truchet
592:Socolar
561:Penrose
556:Gilbert
481:Wythoff
299:1578535
72:pattern
1211:4.8.16
1206:4.8.14
1201:4.8.12
1191:4.8.10
1166:4.6.16
1156:4.6.14
1151:4.6.12
921:Hyper-
906:4.6.12
679:Domino
585:Sphinx
464:Convex
443:Domino
297:
1326:(6.8)
1281:(5.6)
1216:4.8.∞
1186:(4.8)
1181:(4.7)
1176:4.6.∞
1146:(4.6)
1141:(4.5)
1111:4.∞.4
1106:4.8.4
1101:4.7.4
1096:4.6.4
1091:4.5.4
1071:(3.8)
1066:(3.7)
1036:(3.4)
1031:(3.4)
923:bolic
891:(3.6)
847:Semi-
718:Girih
615:Other
295:JSTOR
183:BASIC
1411:8.16
1406:8.12
1376:7.14
1346:6.16
1341:6.12
1336:6.10
1296:5.12
1291:5.10
1246:4.16
1241:4.14
1231:4.12
1221:4.10
1081:3.16
1076:3.14
896:3.12
881:V3.6
807:V4.n
797:V3.n
684:Wang
661:List
627:and
578:and
537:List
452:and
151:Trax
20:and
1441:∞.8
1436:∞.6
1401:8.6
1371:7.8
1366:7.6
1331:6.8
1286:5.8
1251:4.∞
1086:3.∞
1011:3.4
1006:3.∞
1001:3.8
996:3.7
911:4.8
901:4.∞
876:3.6
871:3.∞
866:3.4
802:4.n
792:3.n
765:By
287:doi
255:doi
16:In
1466::
343:.
307:^
293:,
283:20
281:,
251:32
249:,
235:^
165:A
74:.
47:.
24:,
1431:∞
1426:∞
1421:∞
1416:∞
1396:8
1391:8
1386:8
1381:8
1361:7
1356:7
1351:7
1316:6
1311:6
1306:6
1301:6
1271:5
1266:5
1261:5
1256:5
1136:4
1131:4
1126:4
1121:4
1116:4
1026:3
1021:3
1016:3
838:6
833:4
828:3
823:2
787:2
391:e
384:t
377:v
364:"
349:.
289::
262:.
257::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
