At the middle, each way is as likely; toward the ends, one wins and the pattern straightens.
Click a tile to turn it. The address of the page keeps the pattern, to share it.
One tile, turned
In 1704 the Dominican priest Sébastien Truchet, who designed canals and fountains for Louis XIV, published a study of a single square tile, split along its diagonal into a dark and a light half. Laid in its four orientations, it makes an endless variety of patterns, and Truchet counted and catalogued them, as a mathematician would.
In 1987 the metallurgist Cyril Stanley Smith gave the idea a twist: two quarter circles joining the middles of the sides. Every arc meets the arc of the next tile, so the lines never end: laid at random, they wander into meanders, and close into loops of every size. The regions between them can always be colored with only two colors, like a checkerboard of curves.
The same game with a diagonal line gives the maze of
10 PRINT CHR$(205.5+RND(1)); : GOTO 10, one line of
Commodore 64 BASIC that a book was written about in 2012. Push the
Balance away from the middle and order creeps back in:
long diagonals, rows of waves.