Fractal Tilings Based on Successive Adjacent Substitution Rule

Abstract EN

A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal.

f-tilings have complicated structures and strong visual appeal.

However, so far, the discovered f-tilings are very limited since constructing such f-tilings needs special talent.

Based on the idea of hierarchically subdividing adjacent tiles, this paper presents a general method to generate f-tilings.

Penrose tilings are utilized as illustrators to show how to achieve it in detail.

This method can be extended to treat a large number of tilings that can be constructed by substitution rule (such as chair and sphinx tilings and Amman tilings).

Thus, the proposed method can be used to create a great many of f-tilings.