Cool Milk Experiment

This video demonstrates a really cool and simple experiment that can be conducted with milk, food coloring, and dish soap.

http://www.youtube.com/watch?v=Rs8masuu5oE

Watching this pattern change and evolve made me think of chaotic dynamical systems, and their representations like the Mandelbrot set.

I wonder if there is mathematics that models systems like this and describe how they behave?