Eric Weeks - personal pages - computer-generated pictures

# A 2D cellular automata with a twist

weeks/physics.emory.edu

Under the Primordial Soup Kitchen, there is a great picture based on the same principles, but with a neat 3D effect.

## Description

This is one of my favorite pictures because it looks interesting, yet it's a big cheat. I ran the 2-D CA rule that I think is called the voter algorithm -- a cell changes colors if a majority of its neighbors is a different color from it (ie, it changes based on peer pressure). The neighborhood size is large (7 by 7 grid centered on the cell). The edges are held fixed with random states (the entire picture started with random initial conditions).

The cheat comes in from one extra twist. There's also a contour plot underneath all of this. I have taken a function z(x,y) that has nice, smooth hills and valleys, and mapped this so that is ranges from black to white in color. The voter algorithm then just inverts the color, if a cell is "on", or passes the color through, if it is "off". Thus, places where you can see a border between shapes in the picture are due to the voter algorithm. The smooth variations in colors are due to the z(x,y) function.

I choose z(x,y) to be:

z(x,y)=e sin (a*sin(x)+b*cos(y)) + f cos (c*cos(x)+d*sin(y))

with a=1.5, b = 3.0, c = 3.0, d = 3.0, e = 1.0, and f = 1.2