Wednesday, December 3, 2008

Oscillator + Diffusion + Noise = Pattern

(Ring-oscillator with diffusion; x-axis: space, y-axis: time )

After an incredible multi-day pain-in-the ass getting Matlab installed, I'm able to start to explore some of the amorphous computations possible with this toy model I've been playing with. (Previous results came from running Matlab over X which was painfully slow). The above image is a simple ring-oscillator with diffusion and initialized with small random values. The random initial values seem likely in a molecular implementation whereby the inputs to the molecular amplifiers were un-initialized and therefore small stochastic deviations would dominate.

I know that simple processes can produce complicated structures as Wolfram is wont to repeat, but it's still astonishing when you see it. I mean, this thing has no clock, no memory, no boundaries, no initial conditions (just background noise) and a very simple oscillator; it doesn't get much simpler than that. I think the result is kind of beautiful, sinuous, like a tree made of waves. Maybe I'll do my next door panel like this.

All that said, I'm not positive that the patterns aren't an artifact of the integrator. Since I partition space up uniformly, it might be a result of that. I need to run a test where I reduce the spatial step and proportionately reduce the concentrations but my code isn't set up for that yet.

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