Unit Circle Group

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Unit Circle Group Examples

Metal Mesh Unit Circle Group 01	Fireworks Unit Circle Group 02	First Snow Unit Circle Group 03
Ice Crystal Unit Circle Group 04	Organic Web Unit Circle Group 05	Atomic Sprinkles Unit Circle Group 06
Autumn Morning Unit Circle Group 07	Quantum Energy Unit Circle Group 08	Atomic Structure Unit Circle Group 09
Molecular Logic Unit Circle Group 10	Implosion Unit Circle Group 11	Crystal Vortex Unit Circle Group 12
Organic Subspace Unit Circle Group 13	Magnetic Flux Unit Circle Group 14	Metallic Void Unit Circle Group 15
Nanotechnology Unit Circle Group 16

The Unit Circle Group examples are based on an Orbit Trap called the Unit Circle Group. The Unit Circle Group is a stand-alone fractal. It is implemented as an Orbit Trap so it can take advantage of Orbit Trap related features in the Fractal Science Kit, but it does not need the normal orbit processing; i.e., I set the Max Dwell property found in the Orbit Trap Orbit Generation section on the Mandelbrot / Julia / Newton page, to 1, eliminating the normal orbit processing.

Unit Circle Group fractals are described in a paper in the Journal of Mathematics and the Arts called Iterated Mobius transformations by Anne M. Burns, a Professor of Mathematics at the C. W. Post Campus of Long Island University.

Also, see pages 88-89 in the excellent book Indra's Pearls - The Vision of Felix Klein by David Mumford, Caroline Series, and David Wright.