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.
Supported by Tianyuan Foundation, National Nature Science Foundation of China (No. A0324649) and Guangdong Nature Science Foundation (No. 032035).
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Ye, Rs., Ma, J., Li, Hl. (2006). Symmetric Tiling Patterns with the Extended Picard Group in Three-Dimensional Space. In: Nishita, T., Peng, Q., Seidel, HP. (eds) Advances in Computer Graphics. CGI 2006. Lecture Notes in Computer Science, vol 4035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784203_43
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DOI: https://doi.org/10.1007/11784203_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35638-7
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