Tessellations with symmetries of the wallpaper groups and the modular group in the hyperbolic 3-space from dynamics

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Original languageEnglish
Pages (from-to)333-341
Journal / PublicationComputers and Graphics (Pergamon)
Issue number2
Publication statusPublished - Apr 2001


Automatic generation of colored patterns in the hyperbolic 3-space is considered from a dynamical system's point of view. The symmetries of various two-dimensional cross-sections of a tessellation are related to the 17 wallpaper groups and the modular group. The computer images generated in this paper reveal the exotic structures of the tessellations in the hyperbolic 3-space. A color 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. This method can be used to create a great variety of aesthetic symmetrical patterns. © 2001 Elsevier Science Ltd.

Research Area(s)

  • Dynamical systems, Hyperbolic 3-space, Modular group, Wallpaper groups