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Titan I by Ross Hilbert on Flickr.A Mobius Pattern IFS fractal formed from a set of Mobius transformations viewed in the context of a hyperbolic tiling.
A Hyperbolic Tiling replicates a polygon over the hyperbolic plane represented by the Poincare disk in such a way as to form a hyperbolic tiling pattern. The Poincare disk is a model for hyperbolic geometry that maps the hyperbolic plane onto the unit disk.
Created using the Fractal Science Kit fractal generator. See www.fractalsciencekit.com/ for details.
The method used to produce the Mobius Pattern is based on information in the book “Indra’s Pearls - The Vision of Felix Klein” by David Mumford, Caroline Series, and David Wright. For additional details, see David Wright’s “Indra’s Pearls” site (klein.math.okstate.edu/IndrasPearls/).

Titan I by Ross Hilbert on Flickr.

A Mobius Pattern IFS fractal formed from a set of Mobius transformations viewed in the context of a hyperbolic tiling.

A Hyperbolic Tiling replicates a polygon over the hyperbolic plane represented by the Poincare disk in such a way as to form a hyperbolic tiling pattern. The Poincare disk is a model for hyperbolic geometry that maps the hyperbolic plane onto the unit disk.

Created using the Fractal Science Kit fractal generator. See www.fractalsciencekit.com/ for details.

The method used to produce the Mobius Pattern is based on information in the book “Indra’s Pearls - The Vision of Felix Klein” by David Mumford, Caroline Series, and David Wright. For additional details, see David Wright’s “Indra’s Pearls” site (klein.math.okstate.edu/IndrasPearls/).

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