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Automatic generation of aesthetic patterns on fractal tilings by means of dynamical systems

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  • Chung, K.W.
  • Ma, H.M.

Abstract

A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. In this paper, we investigate the classification of fractal tilings with kite-shaped and dart-shaped prototiles from which three new f-tilings are found. Invariant mappings are constructed for the creation of aesthetic patterns on such tilings. A modified convergence time scheme is described, which reflects the rate of convergence of various orbits and at the same time, enhances the artistic appeal of a generated image. A scheme based on the frequency of visit at a pixel is used to generate chaotic attractors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:4:p:1145-1158
    DOI: 10.1016/j.chaos.2004.09.115
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    Cited by:

    1. Zheng, Hongchan & Ye, Zhenglin & Lei, Youming & Liu, Xiaodong, 2007. "Fractal properties of interpolatory subdivision schemes and their application in fractal generation," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 113-123.
    2. 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.

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