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, Š 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 :

escape lines ( for escape radius = 2 ); lines meet at point (-2,0) so thay can't be equipotential lines because each point shuld have only one value of potential
"equipotential" lines ( for escape radius >2 ); lines don't meet

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

( 2 coats of paint). For description see 2D curves page
mirror symmetry around x axis ( M Romera program uses it only in case y:=0 is in the middle of image)

Program Sources (in delphi, without mirror symmetry):