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Volume 2018, Article ID 7315695, 8 pages
Research Article

The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

1School of Mathematics & Physics, Jinggangshan University, Ji’an 343009, China
2Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756, China

Correspondence should be addressed to Peichang Ouyang; moc.361@gnayacf_g

Received 17 October 2017; Accepted 1 January 2018; Published 12 February 2018

Academic Editor: Michele Scarpiniti

Copyright © 2018 Shihuan Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.