END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

Zoom in on interesting regions of the Mandelbrot set with your browser. Computations are done on my quad-core virtual private server:

http://mcm.edsuom.com/

For five points in an X configuration centered at each pixel of the image, inline C code does the fundamental calculation for membership in the Mandelbrot set: periodicity of z = z² + c. If z remains in a stable region of the complex plane or revisits the same point, it is in the Mandelbrot set. The pixel will be assigned a maximum iteration value, which will be mapped to a nearly black, very deep blue. No further points in the X need be computed.

Otherwise, computation proceeds with the other points. The pixel value will be the sum of all iterations required for z to break out of the stable region for each point in the X.

The values are inverted, i.e., subtracted from the maximum value, so that no-escape points (technically, the only points that are actually in the Mandelbrot Set) have zero value and points that escape immediately have the maximum value. This allows simple mapping to the classic image with a black area in the middle. Then they are scaled to the 0.0-1.0 range, and an exponent is applied to emphasize changes at shorter escape times.

Detailed info about how it works is at http://edsuom.com/mcMandelbrot.html