January 27, 2014

Colorful chaol

Soon after I made first version of Visual Chaos app, I started to think about something even more psychedelic than Ising model. What if instead of black and white there were colors? Say, each cell will have a color, and it likes to be surrounded by the cells of the same color.

The simplest way to do it that I thought of is to make use of color wheel:
If colors of two cells are near each other on the wheel, then their energy is minimal. If colors are opposite, energy is at its maximum.

Just as in regular Ising model, from time to time the cell will try to change its color. If cell is cool, it will change to minimize its energy, if cell is hot it may change even if energy goes up. Here is what I got. In the simulation the temperature first goes up, then down again to near zero.

If you see, at the last frame there are some interesting features – little color wheel, points where all colors meet each other, like on the color wheel. Little color wheels cannot be optimized out by lowering temperatures. If you think of it, it’s a deadlock configuration: take red cell, it has orange and magenta neighbors. If it moves to orange, magenta neighbor will object, if it moves to magenta, orange neighbor will be unhappy. The problem cannot be solved by small incremental steps; the only way to solve it is to heat it up, disrupt all colors, then cool down and see if it’s ok. I’ll call such points poles.

Another funny thing about poles is that they come into pairs. Here are few examples of annealing results:

There are poles that go from red to green to blue in clockwise direction, and there are poles that go in counter-clockwise direction. From time to time clockwise and counter-clockwise points collapse and annihilate, for example in this video:

I bet there are a some rules to be learned about how many poles can be formed, and how they evolve over time.

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