structure out of randomness

[miriam_e]

It never ceases to amaze me how easily structure comes out of completely random things. I love the way computers can help throw light on that. Take for example dust-bunnies. Anybody who knows me has probably smiled at my delight with dust-bunnies, those balls of fluff that collect under furniture. Those cute things are a perfect example of order out of randomness. They come about because of little bits of dust being jostled randomly by brownian motion as they settle, and then getting pushed around by breezes when someone walks past or a draft blows under the furniture.

The picture to the right is a very simple computer simulation I did of how the first part happens. Particles of dust settle randomly, while being jiggled around by air molecules. When a particle touches another particle the two stick because of electrostatic forces. This causes those strange branching structures to grow upward. A higher branch has a greater chance of catching more dust particles so it grows preferentially, and as it grows out sideways it shelters areas under it from receiving more settling dust motes, again growing it at the expense of neighboring areas.

I haven't modeled the next part -- shaping the dust into ball-like dust-bunnies, but it is pretty easy to imagine it. A gentle breeze tears a section of this mat away and it rolls up a bit, then another breeze from a different direction preferentially blows the higher section because it is more exposed, and so it rolls another direction adhering more dust to its outer layer and growing more. As it grows it does so in a roughly spherical manner, with this incredibly complex internal structure.

And all of this from random forces. No god. No guiding hand. Intricate structure from just randomness.

Comments

[gothxxangel.livejournal.com]

That's really cool. It reminds me of the chaos theory a bit.

[miriam-e.livejournal.com]

Chaos theory often uses remarkably simple formulas to produce complex, repeatable shapes that look almost random, but generally have some underlying fractal structure. Most of the chaotic stuff I've played with is deterministic, that is if you start with exactly the same conditions it will play out exactly the same way. But there are some that use some randomness and an extreme sensitivity to tiny forces to produce big, unpredictable results (think of a pencil balancing exactly on its point -- you can't predict which way it will fall because tiny air fluctuations will influence the big end result). That's the so-called butterfly effect, where it's been suggested that small changes, even those produced by a butterfly's wings, can affect tropical cyclones. This is why the weather is so hard to predict. It has gazillions of inputs, any one of which could have overwhelming importance.

The dust modeling above is somewhat different from all those. It is very random. The shapes kinda come out of nowhere. I like it because it makes a joke out of the idea that we need a god to produce the complexity we see. Here is amazing complexity from the simplest of random number models.