Raymond Filiatreault wrote:
My questions are: 1) Have different formulas producing the same fractal been reported in the past?
Stephen C. Ferguson once posted to sci.fractals a formula he called "Binomial", which produced exactly the same fractal as a slightly different formula (called "Nova") by a former fractint list member. The reason for this effect were the different initialisations, which perfectly compensated for the difference in the formulas.
2) Are there currently known formulas, other than the z^2+c, producing a replica of the Mandelbrot set? In other words, am I re-inventing the wheel?
Two formulas come to my mind: 1) Stewart's formula (used as "Bifstewart" in Fractint) with: Init: z = c = pixel, Loop: z = c*(z^2) - 1 2) Robert L. Devaney's formula to analyse how a polynomial fractal "morphs" into an exponential one (the following formula approaches exp(z) for n --> infinity): Init: n = 2, z = 1, Loop: z = (1 + z/n)^n Regards, Gerald