Hyperbolic Spirals and Spiral Patterns

Year: 2003 Authors: Douglas Dunham

Core claim

Hyperbolic analogues of standard Euclidean spirals can be defined in the Poincaré model and used to build repeating decorative patterns in hyperbolic tessellations.

Topics

hyperbolic spirals, spiral patterns, Poincaré circle model, regular tessellations

Domains

hyperbolic geometry, polar coordinates, spiral equations, regular tessellations, Celtic patterns, Islamic patterns, decorative pattern design, geometric art

Methods

comparative geometric analysis, model-based rendering, pattern construction, tessellation overlay

Media

Poincaré circle model, Euclidean plane, hyperbolic plane, figures and diagrams

Source status

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