Tessellations in three-dimensional hyperbolic space from dynamics and the quaternions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1181-1197
Journal / PublicationChaos, Solitons and Fractals
Volume12
Issue number7
Publication statusPublished - Jun 2001

Abstract

Automatic generation of coloured patterns in the three-dimensional hyperbolic space is considered from a dynamical systems point of view. Equivariant mappings with the symmetry of the Picard group is constructed. A convergence colour scheme is described, which reveals the convergence rate 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 exotic symmetrical patterns.