Spiral patterns of color symmetry from dynamics

Abstract

This paper explores the esthetics of a kind of logarithmic spiral tilings that has not been investigated. It possesses the form similar to the structure of spiral galaxies, which globally displays the cyclic symmetry. The paper first studies the symmetry group associated with the spiral tiling. Then, using the generators of the group, the construction method of such tilings is analyzed in detail. To create colorful patterns on spiral tilings, a special dynamical system which is compatible with its symmetry group is designed. To promote the esthetic appeal of spiral patterns, a simple but practical strategy for generating patterns of color symmetry is presented. Based on the resulting patterns, several interesting methods are proposed to construct more types of derived spiral patterns.