Patternthree

Patternthree is a term used in digital art and pattern generation to describe a family of tiling and texturing methods that rely on three core building blocks arranged with triadic symmetry. In typical implementations, three motifs—A, B, and C—are defined and combined through a compact rule set that governs their placement, orientation, and color. When the rules are applied recursively, larger patches form that tile the plane without overlaps or gaps, often while preserving a cyclical sequence among the three motifs.

Core concepts include a triadic cycle that advances from A to B to C and back to A, a small rule layer that determines neighbor interactions, and constraints that ensure consistent repetition. Variants differ in how strictly they enforce the cycle and whether color, geometry, or stochastic variation is used to distinguish the motifs. Some designs favor strict periodic tiling with a threefold rotational symmetry; others explore quasi-periodic or randomized assemblies while maintaining the underlying triadic relationship.

Applications span computer-generated textures for games and films, textile and wallpaper design, and educational demonstrations of symmetry and tiling theory. Patternthree can be implemented with grid-based substitution, rule-driven generators similar to L-systems, or procedural noise overlays to modulate color and scale while preserving the three-element structure.

See also: tessellation, tiling, symmetry, L-system, cellular automata.