https://en.wikipedia.org/wiki/Truchet_tiles Jump to content [ ] Main menu Main menu move to sidebar hide Navigation * Main page * Contents * Current events * Random article * About Wikipedia * Contact us Contribute * Help * Learn to edit * Community portal * Recent changes * Upload file * Special pages [wikipe] Wikipedia The Free Encyclopedia Search [ ] Search [ ] Appearance * Donate * Create account * Log in [ ] Personal tools * Donate * Create account * Log in Pages for logged out editors learn more * Contributions * Talk Contents move to sidebar hide * (Top) * 1 Variations Toggle Variations subsection + 1.1 Contrasting triangles + 1.2 Quarter-circles + 1.3 Diagonal * 2 See also * 3 References * 4 External links [ ] Toggle the table of contents Truchet tile [ ] 4 languages * Deutsch * Francais * Russkii * Ukrayins'ka Edit links * Article * Talk [ ] English * Read * Edit * View history [ ] Tools Tools move to sidebar hide Actions * Read * Edit * View history General * What links here * Related changes * Upload file * Permanent link * Page information * Cite this page * Get shortened URL * Download QR code Print/export * Download as PDF * Printable version In other projects * Wikimedia Commons * Wikidata item Appearance move to sidebar hide From Wikipedia, the free encyclopedia (Redirected from Truchet tiles) Square tiles used in graphic design In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling 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.^[1] Truchet tiles were first described in a 1704 memoir by Sebastien Truchet entitled "Memoire sur les combinaisons", and were popularized in 1987 by Cyril Stanley Smith.^[1]^[2] Variations [edit] Contrasting triangles [edit] The tile originally studied by Truchet is split along the diagonal into two triangles of contrasting colors. The tile has four possible orientations. [Truchet_base_tiles_bordered] Some examples of surface filling made tiling such a pattern. With a scheme: [562px-Truchet_ordered_tiling] With random placement: [250px-Truchet_base_tiling] Quarter-circles [edit] A second common form of the Truchet tiles, due to Smith (1987), decorates each tile with two quarter-circles connecting the midpoints of adjacent sides. Each such tile has two possible orientations. Truchet tile The Truchet tile Truchet tile inverse Inverse of the Truchet tile, created by any 90deg rotation or orthogonal flip We have such a tiling: [250px-Truchet_tiling] This type of tile has also been used in abstract strategy games Trax and the Black Path Game, prior to Smith's work.^[1] Diagonal [edit] A labyrinth 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.^[3] The connectivity of the resulting labyrinth can be analyzed mathematically using percolation theory as bond percolation at the critical point of a diagonally-oriented grid. Nick Montfort considers the single line of Commodore 64 BASIC required to generate such patterns - 10 PRINT CHR$(205.5+RND(1)); : GOTO 10 - to be "a concrete poem, a found poem".^[3] [250px-Truchet_labyrinth]A labyrinth generated from diagonal tiles See also [edit] # Wikimedia Commons has media related to Truchet tiles. * Girih tile * Wallpaper group * Wang tile References [edit] 1. ^ ^a ^b ^c Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics, 32 (2): 268-281, doi:10.1016/ j.cag.2007.10.001. 2. ^ Smith, Cyril Stanley (1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy", Leonardo, 20 (4): 373-385, doi:10.2307/1578535, JSTOR 1578535. With a translation of Truchet's text by Pauline Boucher. 3. ^ ^a ^b Montfort, Nick (2012). 10 PRINT CHR$(205.5+RND(1)); : GOTO 10. MIT Press. External links [edit] * Weisstein, Eric W. "Truchet Tiling". MathWorld. * Online Truchet Pattern Generator: https:// truchetpatterns.netlify.app/ * Ibanez, Raul, "The Truchet Tiles and the Diamond Puzzle" * v * t * e Tessellation Periodic * Pythagorean * Rhombille * Schwarz triangle * Rectangle + Domino * Uniform tiling and honeycomb + Coloring + Convex + Kisrhombille * Wallpaper group * Wythoff Aperiodic * Ammann-Beenker * Aperiodic set of prototiles + List * Einstein problem + Socolar-Taylor * Gilbert * Penrose * Pinwheel * Quaquaversal * Rep-tile and Self-tiling + Sphinx * Socolar * Truchet Other * Anisohedral and Isohedral * Architectonic and catoptric * Circle Limit III * Computer graphics * Honeycomb * Isotoxal * List * Packing * Pentagonal * Problems + Domino o Wang + Heesch's + Squaring + Dividing a square into similar rectangles * Prototile + Conway criterion + Girih * Regular Division of the Plane * Regular grid * Substitution * Voronoi * Voderberg By vertex type * 2^n * 3^3.n Spherical * V3^3.n * 4^2.n * V4^2.n * 2^[?] * 3^6 Regular * 4^4 * 6^3 * 3^2.4.3.4 * V3^2.4.3.4 * 3^3.4^2 * 3^3.[?] * 3^4.6 Semi- * V3^4.6 regular * 3.4.6.4 * (3.6)^2 * 3.12^2 * 4^2.[?] * 4.6.12 * 4.8^2 * 3^2.4.3.5 * 3^2.4.3.6 * 3^2.4.3.7 * 3^2.4.3.8 * 3^2.4.3.[?] * 3^2.5.3.5 * 3^2.5.3.6 * 3^2.6.3.6 * 3^2.6.3.8 * 3^2.7.3.7 * 3^2.8.3.8 * 3^3.4.3.4 [120px-Marbl] * 3^2.[?].3.[?] * 3^4.7 [120px-Caris] * 3^4.8 * 3^4.[?] * 3^5.4 * 3^7 * 3^8 * 3^[?] * (3.4)^3 * (3.4)^4 * 3.4.6^2.4 * 3.4.7.4 * 3.4.8.4 * 3.4.[?].4 * 3.6.4.6 * (3.7)^2 * (3.8)^2 * 3.14^2 * 3.16^2 * 3.[?]^2 * 4^2.5.4 * 4^2.6.4 * 4^2.7.4 * 4^2.8.4 * 4^2.[?].4 * 4^5 * 4^6 * 4^7 * 4^8 * 4^[?] * (4.5)^2 * (4.6)^2 * 4.6.12 * 4.6.14 * V4.6.14 * 4.6.16 * V4.6.16 * 4.6.[?] Hyper- * (4.7)^2 bolic * (4.8)^2 * 4.8.10 * V4.8.10 * 4.8.12 * 4.8.14 * 4.8.16 * 4.8.[?] * 4.10^2 * 4.10.12 * 4.12^2 * 4.12.16 * 4.14^2 * 4.16^2 * 4.[?]^2 * 5^4 * 5^5 * 5^6 * 5^[?] * 5.4.6.4 * (5.6)^2 * 5.8^2 * 5.10^2 * 5.12^2 * 6^4 * 6^5 * 6^6 * 6^8 * 6.4.8.4 * (6.8)^2 * 6.8^2 * 6.10^2 * 6.12^2 * 6.16^2 * 7^3 * 7^4 * 7^7 * 7.6^2 * 7.8^2 * 7.14^2 * 8^3 * 8^4 * 8^6 * 8^8 * 8.6^2 * 8.12^2 * 8.16^2 * [?]^3 * [?]^4 * [?]^5 * [?]^[?] * [?].6^2 * [?].8^2 * Retrieved from "https://en.wikipedia.org/w/index.php?title= Truchet_tile&oldid=1303143365" Categories: * Tessellation * Patterns Hidden categories: * Articles with short description * Short description matches Wikidata * Commons category link is on Wikidata * This page was last edited on 29 July 2025, at 09:03 (UTC). * Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply. 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