Fractal Tilings Based on Successive Adjacent Substitution Rule

Peichang Ouyang, Xiaosong Tang, Kwokwai Chung and Tao Yu

Complexity, 2018, vol. 2018, 1-12

Abstract:

A fractal tiling or -tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. -tilings have complicated structures and strong visual appeal. However, so far, the discovered -tilings are very limited since constructing such -tilings needs special talent. Based on the idea of hierarchically subdividing adjacent tiles, this paper presents a general method to generate -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 -tilings.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:6451921

DOI: 10.1155/2018/6451921

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