The Truchet Tile Grammar: A Generative System for Versatile Tile and Pattern Design

This research presents the Truchet Tile Grammar, a generative system for crafting geometric tiles and patterns. Drawing its inspiration from the Truchet Tile, originally introduced by Sebastien Truchet in his seminal work Mémoire sur les Combinaisons (1704) and later expanded upon by C.S. Smith in ‘The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy’ (1987), this grammar establishes shape rules that translate Truchet's conceptual framework into a rule-based specification. The Truchet Tile Grammar comprises three distinct rule sets: 1) Two-Dimensional Tile Rules, 2) Two-Dimensional Pattern Rules, and 3) Extruded Tile Rules. When applied iteratively, this grammar generates extruded two-dimensional tiles. These rule sets can also be independently utilized based on specific design requirements, enhancing the adaptability and utility of this design system.