Jason (jcreed) wrote,
Jason
jcreed

I got kinda frustrated trying to manually come up with a suitably interesting update scheme for a 2+1-dimensional quantum CA thingy, especially since in 1+1-d, it seemed hard not to reinvent Feynman's beautiful checkerboard model. It occurred to me today to just try random ones and see what they do.

Here's a neighborhood scheme:
quad
The notion is, I can just pick any ol' unitary 4x4 matrix, and apply it to a group of four states (every black dot represents one complex number in a big state-vector spanning the whole 2-d spacelike array). On even time steps I apply it in parallel to each group outlined in red, and on odd timesteps to blue. This way hopefully things "circulate" enough.

Here's a quick little js implementation. Click to generate a new random matrix. I made sure the random number generator is deterministic, so you'll see the same sequence of random matrices each time you reload --- the seed number should appear at the top left. I think #2 and #5, #6 are quite pretty.
Tags: javascript, physics
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