Re: Conformal Mapping of Mandelbrot Set

*To*: mathgroup at smc.vnet.net*Subject*: [mg125388] Re: Conformal Mapping of Mandelbrot Set*From*: Roger Bagula <roger.bagula at gmail.com>*Date*: Sun, 11 Mar 2012 04:07:48 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jj9us7$dua$1@smc.vnet.net>

On Mar 8, 1:41 am, JohnBoy1988 <karenannaogil... at hotmail.co.uk> wrote: > Hey, I have a function which should conformally map the Mandelbrot set on to a disc but I can't think of how I would graphically plot this in Mathematica. I have been using Parametric Plot for my conformal mappings so far, but have no idea how I would go about doing it for the Mandelbrot set, any advice would be much appreciated! Thanks I've done a version of a conformal mapping of the Mandelbrot set several ways: The Lapin approach and the Hough transform approach. http://en.wikipedia.org/wiki/Hough_transform This is a re-post of: http://www.groupsrv.com/science/about123754.html "... my interpretation of the bubble chamber image transform called the normal Hough transform first used at Cern in 1959 by P.V. C. Hough. I use the Arctangent like Angle(x,y) to get the angle I call t: {x,y,t}-->{t,x*Cos(t)+y*Sin(t)}" See for the Mandelbrot set approach: http://tech.groups.yahoo.com/group/truenumber/message/4772?var=1 For the Lapin: http://sci.tech-archive.net/Archive/sci.fractals/2005-10/msg00021.html "The "Lapin" is one of the most successful inverse complex plane Mandelbrot/ Julia algorithms in my experience: z'=z^2/(z^2+c) or z'=z^2/(1+c*z^2) instead of z'=1/(z^2+c) type inside out algorithms." Roger L. Bagula