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The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

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  • Shihuan Liu
  • Ming Leng
  • Peichang Ouyang

Abstract

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.

Suggested Citation

  • Shihuan Liu & Ming Leng & Peichang Ouyang, 2018. "The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group," Complexity, Hindawi, vol. 2018, pages 1-8, February.
    • Handle: RePEc:hin:complx:7315695
    DOI: 10.1155/2018/7315695
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    References listed on IDEAS

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    1. Chung, K.W. & Ma, H.M., 2005. "Automatic generation of aesthetic patterns on fractal tilings by means of dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1145-1158.
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    Cited by:

    1. García-Morales, Vladimir, 2019. "A new approach to fuzzy sets: Application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 191-202.

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