Eric Weeks - personal pages - computer-generated pictures

Liquid-crystal-like cellular automata

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This is a cellular automata, simulating a nematic liquid crystal. At each lattice site, imagine you have a little arrow pointing in some direction. Each arrow wants to point in the same direction as its neighbors. Start off with all the arrows pointing in random directions, then try to adjust all the arrows so that they are pointing like their neighbors. Mostly this works; occasionally you can't satisfy all of your neighbors at the same time, and you get cusps.

In the picture above, the color corresponds to the direction that the arrow is pointing at each lattice site. At the cusps (defects), you get a pinwheel of the different colors around a single point.

Note, in a real nematic liquid crystal, the "arrows" are actually double-headed arrows, that is, arrows want to point parallel to the neighboring arrows, but the direction is unimportant other than being parallel. (Arrows pointing straight right are happy being next to arrows pointing straight left, that is, since they are double-headed arrows, there is no distinction between a right-pointing arrow and a left-pointing arrow.)

One additional cheat -- I start with random arrows. This generally results in a certain density of defects. I decided this was too high a density for pretty pictures, so after a while of computing I expand the array by a factor of 2 or 3 in both directions, then compute a little while longer (to help the new result reach a steady state). Thus some of the pictures shown have different densities of defects.

The picture was made using PPM and converted to GIF.

[download] Click here to download software -- "gcc -o lcca lcca.c -lm" to compile. The software is fairly clear, but I am not going to try to explain it here -- if you have questions on how to use it, you can email me if you want.

Other pictures

picture picture

I've often been accused of liking black & white pictures too much, and told to make more color pictures. Well, yeah, color pictures are nice. But you can do some really cool things with black and white! The picture above-right is the same algorithm as discussed above, just using the color to indicate direction. The boundaries between black and white are the places where the arrows are pointing straight right (an arbitrary definition) and the ends of those boundaries are where the defects are, where the colors around a single point are everything from black to white.

Click here to see some more black and white pictures made using the same algorithm, with the only change being the way the colors are mapped to black and white:
small picture small picture small picture small picture


Current address:
Eric R. Weeks
Department of Physics
Emory University
Atlanta, GA 30322-2430