Abstract

A translation is given of Truchet’s 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half-colored tile in various orientations. It embodies an early representation of the principles of combinatorial theory and of crystallographic symmetry including color symmetry. Simple rules of the topology of separation and junction are used to extend Truchet’s concept of directional choice and, by relaxing symmetry rules, to generate diagrams illustrating field/ground relations, the hierarchy of structural freedom and the origin and nature of structural order and disorder in general.

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