Randomness of Dice and the Color of Coffee

Hi,

(let's pretend we are in a deterministic universe)

I'm trying to explain the physics of dice rolls as a mixing process which occurs when numerous external factors influence it's path (so it's chaotic in the sense that it's sensitive to initial conditions).

So, I want to first explain that an ideal robotic arm in a perfect vacuum would roll the same number each time. So the unpredictability of dice is a result of injecting unpredictability through the dices interaction with nature (human hands, air pressure, surface tensions..etc etc etc)

However I'm trying to think of a powerful analogy to explain why the uniform distribution emerges - So, a necessary condition for this would be the fact that the center of gravity is in the middle of the dice and it's symmetric...etc. In my mind those properties are necessary for mixing but not sufficient. The necessary and sufficient conditions for uniform distribution is the mixing part, powered by the variances of nature which come into play. (hands, bounces, air, angles, tensions...etc)

My idea was to show a visual of the possibility space of two dice (as a 2D grid) and coloring each square after each hit on a point in that space, so over time, all squares will tend to be colored equally (or equal color density)). SO, I'd like to show an analog of this process use another natural mixing process such as Brownian motion, say, cream in a coffee cup. So as the cream get's knocked around by interaction with molecules, it will tend to even out across the entire volume of the coffee - again, the same uniform "coloring" emerges.


Is this a terrible analogy in your mind?

Any advice on it, or other ways you'd show this?