Unit Circle Group

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Unit Circle Group Examples

Fractal: Unit Circle Group

Metal Mesh
Unit Circle Group 01

Fractal: Unit Circle Group

Fireworks
Unit Circle Group 02

Fractal: Unit Circle Group

First Snow
Unit Circle Group 03

Fractal: Unit Circle Group

Ice Crystal
Unit Circle Group 04

Fractal: Unit Circle Group

Organic Web
Unit Circle Group 05

Fractal: Unit Circle Group

Atomic Sprinkles
Unit Circle Group 06

Fractal: Unit Circle Group

Autumn Morning
Unit Circle Group 07

Fractal: Unit Circle Group

Quantum Energy
Unit Circle Group 08

Fractal: Unit Circle Group

Atomic Structure
Unit Circle Group 09

Fractal: Unit Circle Group

Molecular Logic
Unit Circle Group 10

Fractal: Unit Circle Group

Implosion
Unit Circle Group 11

Fractal: Unit Circle Group

Crystal Vortex
Unit Circle Group 12

Fractal: Unit Circle Group

Organic Subspace
Unit Circle Group 13

Fractal: Unit Circle Group

Magnetic Flux
Unit Circle Group 14

Fractal: Unit Circle Group

Metallic Void
Unit Circle Group 15

Fractal: Unit Circle Group

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.

 

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