level curves of escape time

Drawing level curves of escape time for complement of M-set






The boundary of the Mandelbrot Set is the limit of the Nth lemniscate
Lemniscate = contour line = border of level set = level curve

The lemniscates were generated and factored in maxima by the following commands:
From the Mandelbrot Set Glossary and Encyclopedia, İ 1987-2004 Robert P. Munafo.

z:0;
for i:1 thru 6 do
(
z:z^2+c,
print(expand(z)),
print(factor(z))
);





Miguel Romera gives an algorithm for drawing contour lines of M-set.
According to Miguel Romera definitions contour lines may be :
Miguel Romera's definition of "equipotential" lines is aproximately true for big escape radius when borders of bands made with discrete (integer) Escape-Time Algorithm = level set method ( LSM ) are aproximating true equipotential lines = level curves of potential

Translations of  BASIC program of M. Romera)
thera are 2 tricks Program Sources (in delphi, without mirror symmetry):

Images: image made with my procedure :

and here is image made with M Romera procedure:







As Inigo Quilez says:
This "method is basically equivalent to drawing a normal escape time picture of Mandelbrot set,
and then detectingthe edges with sobel or lapalacian filter".

Also one can create " these images with the open source fractal tool Xaos, using the mandelbrot formula and the edge detection filter".
Bibliography:

Main page


Autor: Adam Majewski
adammaj1-at-o2-dot-pl
Feel free to e-mail me. (:-))

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