Oh hello guys.
I am in the middle of challenging myself to putting my computer and math skills together, trying to build a small hobby computational cluster. Being interested in fractals for a long time I have been able to calculate silly amounts of Mandelbrot pixels really fast in my new playground ( $10^4$ Mega-pixel images in under 15 minutes right now ). That's more than anyone would have the time to go through. I am now looking for more challenging (computationally intensive) fractals. Plus points if they are easy to split into parallell computations and can render beautiful high-resolution animations.
Here is probably one of the most exciting Mandelbrot images I rendered during those 15 minutes.
Update Just for curiosity I tried running an updated version for 1 terra-pixel ($10^{12}$) (that's one million of images the same resolution of the one above). It seems to take less than 8 hours on my cluster and the size of images (.png lossless compression) total somewhere around 13 GB, but then I had done some additional practical optimizations like transfer queue buffers with ram-drive intermediate storage so with this setting 10 000 images would probably go a bit faster than the 15 minutes we got above.
Diffusion Limited Aggregates also known as DLAs are somewhat difficult to simulate. Here's more information. Basically, you grow a structure by simulating a particle undergoing Brownian motion until it makes contact with the structure. That particle then "sticks", and you repeat the process.
You said you prefer something that can be run in parallel. In that case, you could look into Diffusion Aggregates. Those are aggregates where there is more than one particle simulated at a time.