TITLE: Mandelbrot boundary
QUESTION [10 upvotes]: Is there a sequence of parameterized expressions for the border of all the major bulbs of the mandelbrot set? By major meaning all bulbs with diameter greater than 0.01 for example.  I am interested in generating the major features of the set to apply transformations to it.  I want to create a vector of points of the border (for major features only) for a Matlab type language. I know the parameterized expression for the main cardiod and the period 2 bulb centered at -1.

REPLY [3 votes]: The algebraic solutions one can find :
John Stephenson : "Formulae for cycles in the Mandelbrot set", Physica A 177, 416-420 (1991); "Formulae for cycles in the Mandelbrot set II", Physica A 190, 104-116 (1992); "Formulae for cycles in the Mandelbrot set III", Physica A 190, 117-129 (1992)
Example image using this technique is here :