Geometriae Dedicata
Volume 123, Number 1, 11-63, DOI: 10.1007/s10711-006-9070-3

Original Paper

On hyperbolic once-punctured-torus bundles II: fractal tessellations of the plane

James W. Cannon and Warren Dicks

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Abstract

We describe fractal tessellations of the complex plane that arise naturally from Cannon–Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Keywords  Cannon-Thurston map - Hyperbolic once-punctured-torus bundle - Fractal tessellation - Planar symmetry group

Mathematics Subject Classifications (2000)  57M50 - 57M05 - 20E05 - 20F28

To our wives, Ardyth and Elena.

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