How it works
This is Jeff Jones’ 2010 model of Physarum polycephalum — a single-celled organism with no nervous system that nonetheless finds shortest paths through mazes. Each agent does three things. It deposits a fixed amount of trail into the cell it is standing on. It samples the trail at three points ahead of it, left, centre and right, and turns toward whichever is strongest. Then it steps forward. Between ticks the whole trail map blurs a little and fades.
It is stigmergy: the agents never communicate, they only alter the environment and react to it. The result is a transport network, because a route two agents happen to share gets twice the trail and so attracts a third. Diffusion is what makes that possible at all — without it a deposit is one cell wide and no other agent will ever find it — and decay is what stops it running away. Turn the decay down and the network keeps merging, and merging, until three or four enormous veins are all that is left; that behaviour is real, and the reason the default sits where it does.
One rule in the middle of it decides whether any of this works. When both side sensors beat the centre, the agent turns to a side at random. Turning to the stronger side instead sounds obviously better and is not: it funnels every agent within reach into whichever vein is brightest at that moment, and the sheet ends up with a handful of motorways and nothing else. What is drawn is the trail map rather than the agents — contoured, so the print file is a vector — but the paths of a few agents can be drawn over it, which is the quickest way to see why the veins are where they are.