09-29 Truchet

Agenda:

Modular Elements, Randomized;
Larger Structures Seemingly Emerging Therefrom

Vera Molnár, Untitled (Quatre éléments distribués au hasard), 1959

Anna Carreras, 2021:

10 PRINT

Commodore C64 Basic:

10 PRINT CHR$(205.5+RND(1)); : GOTO 10

Processing (Java):

for (int i=0; i<1000000; i++){
  print ((char)(random(1)<0.5? 47:92));
}

HTML (by Alexander Reben):

data:text/html,<div style=”line-height:1em;word-wrap:break-word;”id=d><script>for(i=0;1e4>i;i++)d.innerHTML+=String.fromCharCode(9585+Math.random()*2);</script>

Truchet Tiles

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square.

[From Mathworld]: A modification of Truchet’s tiles leads to a single tile consisting of two circular arcs of radius equal to half the tile edge length centered at opposed corners. There are two possible orientations of this tile, and tiling the plane using tiles with random orientations gives visually interesting patterns.

By Bleeptrack:

Duotone Truchet Patterns

From Duotone Truchet-Like Tilings, by Cameron Browne:

Multiscale Truchet Patterns

  • Multiscale Truchet Pattern Gradient by Paavo Toivanen:

Wang Tiles & Edge-Matching Puzzles

From [Wikipedia]: First proposed by mathematician Hao Wang in 1961, Wang Tiles are modeled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them. Wang tiles have become a popular tool for procedural synthesis of textures, heightfields, and other large and nonrepeating bidimensional data sets; a small set of precomputed or hand-made source tiles can be assembled very cheaply without too obvious repetitions and without periodicity.

For maze generation:

For game terrain design:

Herringbone Wang Tiles by Sean Barrett:

 

Various Artworks, Experiments, Etc.

By Paul Rickards:

By Rood de Rooij:

By Alexander Reben:

By Andrea Anner and Thibault Brevet:

By Jessica In:

By Joshua Schachter:

By Mario Klingemann:

By Andrew Kudless:

By Roni Kaufman:

By Shane: