Regularity
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== Truchet Tiles == | == Truchet Tiles == | ||
| + | [[File:Truchet-Tiles.jpg|200px|thumb|right|Sébastien Truchet, "Mémoire sur les combinaisons," ''Mémoires de l'Académie Royale des Sciences'', pages 363-372, 1704.]] | ||
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Imagine a square tile, bisected into two triangles, one black, one white. Imagine two such tiles, placed next to one another. Out of this simple configuration emerges a surprising number of possible arrangements. Sixty-four, to be precise, as each tile can be oriented four ways, shifting the apex of the black triangle from corner to corner. Now imagine a whole floor or tapestry covered with a regular pattern of these repeating tiles. This is the power of the Truchet Tile, so named because the Dominican priest Sebastien Truchet first described what he called the "fecundity of these combinations" in 1704, after experimenting with some ceramic tiles he came across at a building site for a chateau near Orléans (Smith 374). | Imagine a square tile, bisected into two triangles, one black, one white. Imagine two such tiles, placed next to one another. Out of this simple configuration emerges a surprising number of possible arrangements. Sixty-four, to be precise, as each tile can be oriented four ways, shifting the apex of the black triangle from corner to corner. Now imagine a whole floor or tapestry covered with a regular pattern of these repeating tiles. This is the power of the Truchet Tile, so named because the Dominican priest Sebastien Truchet first described what he called the "fecundity of these combinations" in 1704, after experimenting with some ceramic tiles he came across at a building site for a chateau near Orléans (Smith 374). | ||
| − | [[File:Truchet-Tiles.jpg|200px|thumb|right|Sébastien Truchet, "Mémoire sur les combinaisons," ''Mémoires de l'Académie Royale des Sciences'', pages 363-372, 1704.]] | + | 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). |
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| + | 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. | ||
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