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...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/6451921 |
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| _version_ | 1832548731198636032 |
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| author | Peichang Ouyang Xiaosong Tang Kwokwai Chung Tao Yu |
| author_facet | Peichang Ouyang Xiaosong Tang Kwokwai Chung Tao Yu |
| author_sort | Peichang Ouyang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5e9259d1cf1448768863223947c0142a |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-5e9259d1cf1448768863223947c0142a2025-02-03T06:13:13ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/64519216451921Fractal Tilings Based on Successive Adjacent Substitution RulePeichang Ouyang0Xiaosong Tang1Kwokwai Chung2Tao Yu3School of Mathematics and Physics, Jinggangshan University, Ji’an, ChinaSchool of Mathematics and Physics, Jinggangshan University, Ji’an, ChinaDepartment of Mathematics, City University of Hong Kong, Kowloon, Hong KongSchool of Mathematics and Physics, Jinggangshan University, Ji’an, ChinaA 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.http://dx.doi.org/10.1155/2018/6451921 |
| spellingShingle | Peichang Ouyang Xiaosong Tang Kwokwai Chung Tao Yu Fractal Tilings Based on Successive Adjacent Substitution Rule Complexity |
| title | Fractal Tilings Based on Successive Adjacent Substitution Rule |
| title_full | Fractal Tilings Based on Successive Adjacent Substitution Rule |
| title_fullStr | Fractal Tilings Based on Successive Adjacent Substitution Rule |
| title_full_unstemmed | Fractal Tilings Based on Successive Adjacent Substitution Rule |
| title_short | Fractal Tilings Based on Successive Adjacent Substitution Rule |
| title_sort | fractal tilings based on successive adjacent substitution rule |
| url | http://dx.doi.org/10.1155/2018/6451921 |
| work_keys_str_mv | AT peichangouyang fractaltilingsbasedonsuccessiveadjacentsubstitutionrule AT xiaosongtang fractaltilingsbasedonsuccessiveadjacentsubstitutionrule AT kwokwaichung fractaltilingsbasedonsuccessiveadjacentsubstitutionrule AT taoyu fractaltilingsbasedonsuccessiveadjacentsubstitutionrule |