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Introducing the Kalibrot



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=7867

Want to add some texture to those low-iteration Mandelbrots? Kalibrot to the rescue! Kaliset patterns replace boring old iteration bands, seamless and brimming with detail.

I'm going to take a guess. When the first iterator escapes, move on to a second iterator. Clever.

The effect is cool, but it sounds slow with all those transcendental functions.

My scheme for coloring the thin "tendrils" around a Mandelbrot/Julia set involves applying a non-integer power to the Distance Estimate (DE) value, but only for pixels that are very close to a Mandelbrot/Julia set point. It only has to calculate a non-integer power on a small percentage of the pixels in a plot, and then only for a single distance value of each pixel. I'm not doing multiple transcendentals on each iteration of each pixel like it sounds like you are doing.

How much slower is your Kalibrot algorithm over a straight escape-time algorithm?

My scheme enables me to feather the boundary of the Mandelbrot set and apply mathematical anti-aliasing. I can get results like this:

http://www.pbase.com/duncanc/image/91190108

I was trying to duplicate the lacy look of the B&W images in the seminal books "The Beauty of Fractals" and "The Science of Fractal images". I think I got it: