Smooth spectrum for Mandelbrot Set rendering

Question

I\'m currently writing a program to generate really enormous (65536x65536 pixels and above) Mandelbrot images, and I\'d like to devise a spectrum and coloring scheme that do

Answer 1

Seems simple to do by trial and error. Assume you can define HSV1 and HSV2 (hue, saturation, value) of the endpoint colors you wish to use (black and white; blue and yellow; dark red and light green; etc.), and assume you have an algorithm to assign a value P between 0.0 and 1.0 to each of your pixels. Then that pixel's color becomes

(H2 - H1) * P + H1 = HP
(S2 - S1) * P + S1 = SP
(V2 - V1) * P + V1 = VP

With that done, just observe the results and see how you like them. If the algorithm to assign P is continuous, then the gradient should be smooth as well.