Unit Circle Group 

Unit Circle Group ExamplesThe Unit Circle Group examples are based on an Orbit Trap called the Unit Circle Group. The Unit Circle Group is a standalone 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 8889 in the excellent book Indra's Pearls  The Vision of Felix Klein by David Mumford, Caroline Series, and David Wright. 
Copyright © 20042019 Ross Hilbert 