Concise Methods to Generate Fractal Tilings

摘要

This paper shows that a new method, similar to that used to construct irregular tilings, can be employed to construct fractal tilings. Five main methods, including Escher's tiling pictures methods and the Conway criterion are used to create the fractal tilings. Two famous fractal tilings with computer simulation graphs are presented to clarify the arguments. These methods complements iteration methods, and also provide a concise way to check whether a fractal disk can tile the plane. Furthermore, the problem of non-self-intersection of a fractal curve is discussed, which is important in our work and in the problem of heat equations on a region with a fractal boundary.