TILINGS OF THE PLANE ARISING FROM ITERATED FUNCTION SYSTEMS GENERATED BY THREE SIMILARITY TRANSFORMATIONS (Integrated Research on Random Dynamical Systems and Multi-Valued Dynamical Systems)

Abstract

A similarity tiling is a partition of the plane by tiles all similar to each other with pairwise disjoint interiors. We investigate similarity tilings arising from iterated function systems generated by two or three similarity transformations. To find parameters of the generating similarity transformations, we execute search programs to find candidates of the complex ratios, and find locations of the centers by using Fractal Gazer, a computer program developed by the author.