There is by the way this chaos library of Pd classes by Ben Bogart and Michael McGonagle. The library is about fractals. An entry point for help is flatspace/readme-fractals.pd.

The actual calculations are done within the c objects, so in order to know how they are done you need to read the through the source code. Using the library would be very instructive as well, of course.

Katja.

I don't see how I missed this. Here is a patch that has the mandelbrot in an expr.
It is an old patch and I have actually changed some things since then you can more recent see videos on my youtube page.

http://sites.google.com/site/billystiltner/Astronauts/mandel3.pd

I have been into chaos and sound for quite sometime.
I like mapping the orbits directly to sound as well as generating notes with the orbits. The patch in the link is the generate notes from orbits kind.

The patch was inspired by Elaine Walker's max patch in her thesis on chaos melody maker. It is a good read if you are interested in fractals and music.
http://www.ziaspace.com/elaine/chaos/

Thanks for sharing your patch and the pointer to Elaine's thesis. Together, they are very informative. I found it impossible to find an interesting fractal 'by hand' though. Everytime when a pattern sounds interesting, it's flying to the stars and reset, being not part of the Mandelbrot set. The logistic map function is much easier to handle, like Elaine mentioned in her thesis.

Katja

http://www.geocities.ws/billy_stiltner/music/pd/manit.pd is an abstraction that accepts as input:

a bang to perform an iteration

a bang to restart orbit

k,l(real and imag of C)

boundary ie. 4 if the escape boundary has a radius of 2

and numits - 0=free running

outputs are:

itnum(resets to 0 on escape or numits reached)

x,y(real and imag of Z)

xesc,yesc(real and imag of Zescape) only when an orbit escapes boundary

a bang when an orbit escapes

a bang when an orbit reaches numits

to put x or y to notes use this expr

[expr (($f1 + 4) / 8 * $f2) + $ f3]

f1 = x or y(make one expr ezch for x and y)
$f2 = scale factor (this stretches or compresses the range of notes)
$f3 = offset(this transposes the notes up or down a step)

output is a note number which can feed a mtof or table lookup for nonstandard tunings.

You could also use the old scaling algorithm.

This implementation uses abs( in the boundary check to get rid of some of the flying off to space notes)

One of these days I should make an example and help file. Curently the only patches I have using this have way too many other patches and tangled messes of wires to submit as an example.