Mathematics and beauty-VIII. Tesselation automata derived from a single defect

Abstract

To help characterize complicated physical and mathematical structures and phenomena, computers with graphics can be used to produce visual representations with a spectrum of perspectives. In this paper, unusual "tesselation automata" (TA) are presented which grow according to certain symmetrical recursive rules. TA are a class of simple mathematical systems which exhibit complex behavior and which are becoming important as models for a variety of physical processes. This paper differs from others in that its focuses on symmetrical TA derived from a single defect, and reader involvement is encouraged by giving "recipes" for the various chaotic forms which represent a visually striking and intricate class of shapes. © 1989.