Regularity
From Maze
(Difference between revisions)
(Truchet and Randomness) | (→Truchet Tiles) | ||
| Line 11: | Line 11: | ||
Matching a single Truchet tile with another, and another, and another, and so on, a designer is able to create an incredible array of patterns. The interplay between the direction of each tile and the varying repetition of black and white -- of positive and negative -- produces designs that can range from grid-like patterns to mesmerizing, almost three-dimensional mazes. Unlike earlier Islamic patterns or Celtic designs, which both relied on multiple-sized shapes, the Truchet tile uses only a single size and a single shape (Smith 378). In his original 1704 essay, Truchet provided examples of thirty different patterns, barely evoking the aesthetic possibilities of his tiles, though he notes that he "found too great a number to report them all" (Smith 374). Truchet's work would be the inspiration for a latter book, Douat's modestly named ''Methode pour faire une infinite de desseins differents,'' which in turn had a considerable impact on 18th century European art (Smith 373). | Matching a single Truchet tile with another, and another, and another, and so on, a designer is able to create an incredible array of patterns. The interplay between the direction of each tile and the varying repetition of black and white -- of positive and negative -- produces designs that can range from grid-like patterns to mesmerizing, almost three-dimensional mazes. Unlike earlier Islamic patterns or Celtic designs, which both relied on multiple-sized shapes, the Truchet tile uses only a single size and a single shape (Smith 378). In his original 1704 essay, Truchet provided examples of thirty different patterns, barely evoking the aesthetic possibilities of his tiles, though he notes that he "found too great a number to report them all" (Smith 374). Truchet's work would be the inspiration for a latter book, Douat's modestly named ''Methode pour faire une infinite de desseins differents,'' which in turn had a considerable impact on 18th century European art (Smith 373). | ||
| − | Yet all of Truchet's and Douat's examples are regular patterns, symmetrical and repetitive. The mathematician Cyril Stanley Smith observes that even more compelling designs can be generated from Truchet tiles if "dissymmetries" are introduced. What happens when the regularity of a Truchet pattern is interrupted by randomness? Smith provides one example, a block of Truchet tiles arranged at random. | + | Yet all of Truchet's and Douat's examples are regular patterns, symmetrical and repetitive. The mathematician Cyril Stanley Smith observes that even more compelling designs can be generated from Truchet tiles if "dissymmetries" are introduced. What happens when the regularity of a Truchet pattern is interrupted by randomness? Smith provides one example, a block of Truchet tiles arranged at random: |
| + | |||
| + | [[File:Truchet-Tiles-Randoms.jpg|500px|center|Smith, Cyril Stanley, and Pauline Boucher. “The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy.” Leonardo 20.4 (1987) : 373-385.]] | ||
| + | |||
| + | The latices of a grid are still visible, but randomness has made its mark, leaving imperfections that disrupt any nascent pattern. Unlike the examples Truchet and Douat give, there is no resolution to the structure. Smith continues to push the limits of the Truchet tiles' regularity by omitting colors from the tiles, leaving only the black diagonal line. Suddenly the four orientations of any given tile have been reduced to two. Smith does this trick with random array of Truchet tiles pictured above: | ||
| + | |||
[MORE COMING] | [MORE COMING] | ||
