And now for something completely different...
Give it a few time steps to settle down, but what you will soon see is everyone active, then red (inactive) ants appearing on the edge. Eventually the activity will shrink down to the middle and perhaps die away. But very soon after, one will become active again and you'll see the wave of activity spread until everyone is jumping. If you were bored enough to count the number of timesteps the 'ants' are active, you'd find it's very nearly the same every time. That means, periodicity! An emergent property of the individual ants. Here is a graph of activity versus time for this, in which the periodicity is very evident.

Now this is the most rudimentary intro to this. There are five parameters that vary continuously and grid size and geometry and ant density can all be changed. On top of that, this can be done by having each ant driven by a chaotic oscillator, getting rid of the random activator, which pleases the deterministic nonlinear dynamicist in us all.

[Here's the java code.] You are free to use and modify it.