Hierarchical Modular Systems with Elements of Folk Art

Hierarchical modular systems are composed of identical elements assembled by systematic rules based on rotational group. The systems are characterized by hierarchical symmetries and their regular outlines defined by the last rules. To introduce fundamental an element of Japanese folk art into an initial module of our system, we can form various hierarchical symmetric patterns composed of identical elements. Since outline of a pattern is defined by a last rule, it can be mapped into regular or semi-regular tessellation and polyhedron. We show various examples from traditional uniform patterns to self-similar patterns.