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Just reading about chaos theory/sensitive dependance on initial conditions in James Gleick's Chaos,also information online, and I was wondering what programs are out there for modelling such non-linear systems?
I came up with an idea and would like to be able to model it.
Basically I thought of a pot of white paint with a single dot of red paint. A motorised mixing rod is inserted and rotates at a fixed speed until all the paint is mixed,(topological mixing) making pink paint (the infinity point)
The initial condition could be the placement of the rod,different positions giving different results.
Any ideas?

Look at this:
The Kelvin-Helmholtz instability (http://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_instability)
(http://upload.wikimedia.org/wikipedia/commons/8/8e/KHI.gif)
I think, that's a very nice fractal from fluid dynamics :)

now thas nice, and I'm sure i can see some julias in there!

there are even more nice fractals which afaik all are related to each other

http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Taylor_instability
http://en.wikipedia.org/wiki/Richtmyer%E2%80%93Meshkov_instability
http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability

All of them should be modelable more or less easily, I guess :)

The Rayleigh-Taylor one even includes a formula which you might be able to use :)

Oh, and don't forget the thermodynamic fractals....
http://en.wikipedia.org/wiki/Thermodynamics
Most likely a whole set of fractals is included in them - just look at that tiny (:P) "See also"-section.
At least one of them definitely is a fractal: Brownian motion :)

Gotta love that Brownian Motion link!  O0

I'm glad someone appears to be enjoying it  :). I am currently in the process of trying to find and describe a break point between Brownian motion and directed motility for bacteria. Not as fun as it sounds, but nature loooves those breaks in symmetry (i.e. from randomness into order in this case.) so I guess I'll have to tag along for the ride.

this is quite beautiful
what an odd coincedence, I've just recently became interested in fluid dynamics in autodesk maya. I suggest that all of u guys download maya and begin using the fluid 3d node. I did some work with it a few weeks ago. Everything that was mentioned in this thread is present within the parameters of the fluid 3d grid in maya. You guys would have a lot of fun with it. Once youtube is finished uploading my fluid test, I'll upload it here  :D

Where do we get this maya from?

http://www.youtube.com/watch?v=skzNZP0FsXg&feature=player_embedded

in the dynamics tab there is an option to create a 2d or 3d fluid box which you can create your fluid inside. this effects has been used in movies for explosions, water simulations and harry potter like spell effects. More than likely though if fluid 3d is being used for production purposes, the plug-in "Realflow" would be used to test out and bake the dynamics in its separate program and then brought back into Maya. This is because fluids are so slow in Maya, wheres Realflow dedicate all of its memory to dynamics and nothing else. I think it might run on the GPU as well. Search fluid 3d and 2d in youtube and you should be able to find a tutorial on how to get it started. I recommend you search "realflow" as well just to see how cool it is.