The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

By constructing invariant mappings associated with wallpaper groups, this paper presents a simple and efficient method to generate colorful wallpaper patterns. Although the constructed mappings have simple form and only two parameters, combined with the color scheme of orbit trap algorithm, such map...

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Bibliographic Details
Main Authors: Shihuan Liu, Ming Leng, Peichang Ouyang
Format: Article
Language:English
Published: Hindawi-Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/7315695
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spelling doaj-6639602dbb87449cb1f7c8cd66a66d8c2020-11-25T00:48:41ZengHindawi-WileyComplexity1076-27871099-05262018-01-01201810.1155/2018/73156957315695The Visualization of Spherical Patterns with Symmetries of the Wallpaper GroupShihuan Liu0Ming Leng1Peichang Ouyang2School of Mathematics & Physics, Jinggangshan University, Ji’an 343009, ChinaSchool of Mathematics & Physics, Jinggangshan University, Ji’an 343009, ChinaSchool of Mathematics & Physics, Jinggangshan University, Ji’an 343009, ChinaBy constructing invariant mappings associated with wallpaper groups, this paper presents a simple and efficient method to generate colorful wallpaper patterns. Although the constructed mappings have simple form and only two parameters, combined with the color scheme of orbit trap algorithm, such mappings can create a great variety of aesthetic wallpaper patterns. The resulting wallpaper patterns are further projected by central projection onto the sphere. This creates the interesting spherical patterns that possess infinite symmetries in a finite space.http://dx.doi.org/10.1155/2018/7315695
collection DOAJ
language English
format Article
sources DOAJ
author Shihuan Liu
Ming Leng
Peichang Ouyang
spellingShingle Shihuan Liu
Ming Leng
Peichang Ouyang
The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
Complexity
author_facet Shihuan Liu
Ming Leng
Peichang Ouyang
author_sort Shihuan Liu
title The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
title_short The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
title_full The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
title_fullStr The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
title_full_unstemmed The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group
title_sort visualization of spherical patterns with symmetries of the wallpaper group
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2018-01-01
description By constructing invariant mappings associated with wallpaper groups, this paper presents a simple and efficient method to generate colorful wallpaper patterns. Although the constructed mappings have simple form and only two parameters, combined with the color scheme of orbit trap algorithm, such mappings can create a great variety of aesthetic wallpaper patterns. The resulting wallpaper patterns are further projected by central projection onto the sphere. This creates the interesting spherical patterns that possess infinite symmetries in a finite space.
url http://dx.doi.org/10.1155/2018/7315695
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AT peichangouyang thevisualizationofsphericalpatternswithsymmetriesofthewallpapergroup
AT shihuanliu visualizationofsphericalpatternswithsymmetriesofthewallpapergroup
AT mingleng visualizationofsphericalpatternswithsymmetriesofthewallpapergroup
AT peichangouyang visualizationofsphericalpatternswithsymmetriesofthewallpapergroup
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