I gave a talk a couple weeks ago which featured both cellular automata and the Collatz sequence as examples. Then Chuck Moore spoke on his GreenArrays chip with 144 tiny computers on it. I wondered what would happen if each of those little machines were calculating the Collatz sequence. Well, that wouldn't do much. But what if something in that calculation triggered a computer to send information to its neighbors?
So here's the setup:
An NxN grid of cells.
Each cell contains an integer K.
If K is odd replace it with 3K+1.
If K is even replace it with K/2.
Unless K is divisible by 8: then we replace with it 1 and add 1 to each neighbor.
In this particular example we're also "bouncing" 1s off the edges back into the cell. Neighbors are a la von Neumann.