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Fractal Tilings Based on Successive Adjacent Substitution Rule

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  • Peichang Ouyang
  • Xiaosong Tang
  • Kwokwai Chung
  • Tao Yu

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.

Suggested Citation

  • Peichang Ouyang & Xiaosong Tang & Kwokwai Chung & Tao Yu, 2018. "Fractal Tilings Based on Successive Adjacent Substitution Rule," Complexity, Hindawi, vol. 2018, pages 1-12, July.
    • Handle: RePEc:hin:complx:6451921
    DOI: 10.1155/2018/6451921
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