Coding and generating complex periodic patterns

This paper presents a method of coding and generating infinite classes of comlex periodic geometric pattern found in various cultures. The method uses a pattern code for the known symmetry groups and is based on the infinite classes of subdivisions of the fundamental regions of each symmetry group. The subdivisions provide a skeletal grid from which selected point, line or polygonal sequences can be extracted to produce an infinite variety of geometric patternswithin a symmetry group. Surprisingly, many complex architectural patterns from different periods and cultures, notably those from historic Islamic buildings, and Chinese window lattices, can be systematically obtained by this method. The pattern-codes provide a basis for generation of simple and complex geometric patterns, and their transformation from one to another. Some directions for systematic transformations based on meta-structural principles are outlined.