Creeper is a semi-stochastic process which is based on a two dimensional Drunkard's Walk.

There is initially a 'seed' cell. A Drunkard's Walk process is started from each of the seed's neighbour cells. When a drunkard arrives at the seed cell, that process is discontinued. When only one drunkard process still remains it is discontinued and the cell from which it started is turned into a seed.

Now Drunkard's Walk processes are started from all neighbours of the pair of seed cells. As each drunkard arrives at either seed its process is discontinued. Once again, the starting point of the last remaining drunkard is turned into a seed, and new Drunkard's Walk processes are started from the neighbours of the three seeds. This cycle continues ad infinitum.

In the simulation below, there is a slight cheat. If any of the walk processes survive for 1000 steps, the process is stopped and the cell from which it started is turned into a seed. This means that more than one new seed can appear in each cycle, but it turns out that 98 - 99 % of the walk processes terminate before taking 1000 steps. The new seeds for each cycle are created synchronously.

Anyway, here's the simulation....