Fractal Tilings Based on Successive Adjacent Substitution Rule

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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Main Authors: Peichang Ouyang, Xiaosong Tang, Kwokwai Chung, Tao Yu
Format: Article
Language:English
Published: Hindawi-Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/6451921
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spelling doaj-5e9259d1cf1448768863223947c0142a2020-11-25T00:18:33ZengHindawi-WileyComplexity1076-27871099-05262018-01-01201810.1155/2018/64519216451921Fractal 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
collection DOAJ
language English
format Article
sources DOAJ
author Peichang Ouyang
Xiaosong Tang
Kwokwai Chung
Tao Yu
spellingShingle Peichang Ouyang
Xiaosong Tang
Kwokwai Chung
Tao Yu
Fractal Tilings Based on Successive Adjacent Substitution Rule
Complexity
author_facet Peichang Ouyang
Xiaosong Tang
Kwokwai Chung
Tao Yu
author_sort Peichang Ouyang
title Fractal Tilings Based on Successive Adjacent Substitution Rule
title_short 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_sort fractal tilings based on successive adjacent substitution rule
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2018-01-01
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.
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
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