Fractal Tilings Based on Successive Adjacent Substitution Rule
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.
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1988 ◽
Vol 03
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pp. 1321-1341
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1976 ◽
Vol 34
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pp. 538-539
1992 ◽
Vol 50
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pp. 694-695
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2019 ◽
Vol 25
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pp. 256-279
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