The lab

Slime Mold

Physarum polycephalum is a single-celled organism that solves optimization problems without a brain, without a plan, without any central control. Place food sources on the surface and watch it build efficient transport networks — the same networks that, in the famous Tero et al. experiment, closely matched the Tokyo rail system.

Physarum polycephalum · Jones 2010 agent model · stigmergic optimization

agents: 5000

food sources: 6

frame 0

running

click to place food sources

Sensor Angle 45°

Sensor Distance 9

Turn Speed 45°

Decay Rate 0.95

Agent Count 5000

Diffuse Radius 1

Physarum polycephalum is a slime mold — a single-celled organism that can grow to several square feet. It has no nervous system, no central processing, no plan. And yet, when researchers at Hokkaido University placed oat flakes at positions corresponding to cities around Tokyo, the organism grew a network of tubular connections that closely matched the actual rail system. Not approximately. Closely. The same topology, similar redundancy, comparable efficiency. A cell with no brain solved a problem that took human engineers decades.

This simulation uses the agent-based model proposed by Jeff Jones in 2010. Thousands of virtual particles wander a two-dimensional surface. Each agent carries three sensors — one ahead, one to the left, one to the right — that sample a chemical trail map. The agent turns toward the strongest signal and deposits a small amount of chemical at its current position. The trail map decays and diffuses each frame. That is everything: sense, turn, move, deposit. No pathfinding algorithm. No global optimization. No coordination between agents. And yet from these purely local rules, coherent networks emerge. Agents reinforce each other’s trails through a feedback loop — more traffic means more chemical, more chemical means more traffic — and the result is a self-organizing transport network that prunes inefficient routes over time.

What I find remarkable is the pruning. Watch carefully after the initial expansion phase. The organism does not simply connect everything to everything. It builds redundant paths first, then gradually starves the less-trafficked ones as the chemical decays faster than it is replenished. What remains are the efficient routes — the ones carrying enough flow to sustain themselves. This is the same principle behind ant colony optimization, but Physarum does it with a continuous network rather than discrete paths. The result approximates a Steiner tree: a minimum-cost network connecting all the food sources. Not because the organism knows what a Steiner tree is. Because the dynamics converge there.

Click the canvas to place food sources. Try the Tokyo preset to see the organism approximate a rail network. Watch for the three phases: initial expansion (agents fill the space), path formation (trails brighten between food sources), and pruning (dim trails fade as efficient routes consolidate). Adjusting the decay rate changes how aggressively the organism prunes — lower values create sparser, more tree-like networks.