The Mandelbrot Set

Mandelbrot set detail, (-1.37791351+0.01647188i) to (-1.37791307+0.01647232i), maxiter=6000

Given that I had intended this site to be more about science than maths, the number of Mandelbrot pages is slightly embarassing. However, one can learn computer science from the Mandelbrot Set, as well as maths.

So we have:

And we have covered

whilst producing lots of pleasant images.

You will find better / faster Mandelbrot Set programs on the web easily, but the point of this exercise was to learn as little whilst working with such programs. The TK codes (serial and parallel) are good enough to be useable, and if one needs arbitrary precision and can compile the mixed python/C version, then that is also almost useable.

There is plenty of scope for taking these programs further. One obvious possibility would be a program which used standard, and fast, double precision arithmetic when that was sufficient, but switched to one of the (slow) arbitrary precision versions when that became necessary.