Symmetric tiling patterns with the extended picard group in three-dimensional space

  • Authors:

  • Rui-song Ye;Jian Ma;Hui-liang Li

  • Affiliations:

  • Department of Mathematics, Shantou University, Shantou, Guangdong, P.R. China;Department of Mathematics, Shantou University, Shantou, Guangdong, P.R. China;Department of Mathematics, Shantou University, Shantou, Guangdong, P.R. China

  • Venue:
  • CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
  • Year:
  • 2006

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Abstract

Automatic generation of tiling patterns with the symmetry of the extended Picard group in three-dimensional hyperbolic space is considered. We generate the patterns by repeating the fundamental patterns created in the fundamental region to all other equivalent regions. We also produce such a kind of tiling patterns in the unit sphere by conformal mappings. The method provides a novel approach for devising exotic symmetric tiling patterns from a dynamical system's point of view.