The Chaos Game

Even though I am neither a mathematician or a physicist, I am fascinated by chaos theory. And that has nothing to do with the pretty pictures it mostly generates.
I probably don't even understand half of the concept of it, but still the idea behind it is rather appealing: all the order in the world depends on randomness. Or: disorder always seems to have a orderly basis.

The chaos game was one of the eye-openers for me. The idea consists of three simple steps:
1. Take 3 points in a plane, and form a triangle
2. Randomly select any point inside the triangle and move half the distance from
that point to any of the 3 vertex points. Plot the current position.
3. Repeat from step 2.

After a little while, you'll eventually end up with the figure above: the so-called Sierpinski triangle (or gasket). No matter where you start, no matter which directions you start off in. If you'd take another operation for step 2, you get another shape. Mostly fractal. For instance, you might end up with that famous fern-leaf shaped thingie. But it's not about form as such, it's about creating order from chaos.

But look at it from the other way around: imagine you have a shape, any shape. If you find the right algorithm behind it - the "constructing" algorithm - and feed it backwards, you'll end up with a random point. You never know where you'll end up... Or, you never know where the order came from...

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