Eric Weeks - personal pages - computer-generated pictures Liquid-crystal-like cellular automata

weeks/physics.emory.edu

Description

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.

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