Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, "Why?" Oh dear, that is never a good question, so let's try "Why shouldn't they?"
The obvious observations are that the water is very hot when the milk is added, so we expect the "coffee particles" (non-milk part) to have a higher velocity relative to the "milk particles". Secondly, the coffee part, having been recently stirred, is often still rotating (clockwise in my case). Finally, the image we observe is a projection of some distinct portion of a "top layer" of the milk and coffee mixture.
Add diffusion into the mix and it really seems like some crazy stuff should go down! But I'm afraid I'm not satisfied. Why physics.SE... why?