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:
"... 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)