Mobius Transformations 

Mobius Transformations OverviewSeveral of the Fractal Science Kit fractal generator builtin programs make use of Mobius transformations, also called linear fractional transformations. Mobius transformations are complex transformations in the form: f(z) = (A*z + B) / (C*z + D) The numbers A, B, C, and D are complex numbers. The input to the function (z) and the function result are both complex. Mobius transformation can be classified as 1 of 4 types: elliptic, hyperbolic, loxodromic, or parabolic. The builtin macros define a Mobius Object and a collection of Mobius Functions. While the understanding of Mobius transformations is not a prerequisite to using the application, it is an interesting and rewarding area of mathematics that can be used to produce beautiful fractals and is highly recommended. The following web sites provide an introduction to Mobius transformations: Eric W. Weisstein. "Linear Fractional Transformation." From MathWorldA Wolfram Web Resource.
From Wikipedia, the free encyclopedia. The following books cover Mobius transformations in detail: Indra's Pearls  The Vision of Felix Klein David Mumford, Caroline Series, David Wright
Visual Complex Analysis Tristan Needham
Introduction to Geometry H. S. M. Coxeter, F. R. S.
Geometry David A. Brannan, Matthew F. Esplen, Jeremy J. Gray
Geometry  A Comprehensive Course Dan Pedoe 
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