Slime Mold: A Brainless Cell That Builds Rail Networks

One giant cell, no nervous system

Physarum polycephalum is not a fungus, a plant or an animal — it is a plasmodial slime mold, a single cell that can grow to cover a dinner plate while containing millions of nuclei sharing one shared cytoplasm, with no cell walls dividing it internally. It has no brain, no nerves, no muscles in the animal sense. Yet when it forages, it does something that looks remarkably like planning: it spreads outward from a food source, explores in every direction, then withdraws from unproductive branches and thickens the ones that are working, until what remains is a lean, efficient network connecting every food source it has found.

Sense, move, deposit: the whole rule set

The computational model that reproduces this behaviour, developed by Jeff Jones in 2010, does not simulate the organism's internal biochemistry at all. Instead it represents Physarum as thousands of independent particle agents moving over a shared 2D trail field. Each agent follows three steps every tick:

1. SENSE  -- read the trail field at three points ahead of the agent:
            front-left, straight-ahead, front-right (a fixed sensor angle
            and distance from the agent's current heading)
2. TURN   -- rotate toward whichever sensor reads the highest trail value;
            if straight-ahead is highest, keep going; if none stand out,
            turn by a small random amount
3. MOVE + DEPOSIT -- step forward and drop trail chemical at the new
            position; every cell of the field decays and diffuses a
            little each tick

That is the entire algorithm. No agent knows where any food source is, how many other agents exist, or what shape the final network will take. The behaviour is stigmergic — coordination happens entirely through the shared environment, the trail field, rather than through direct communication. An agent that happens to wander toward a food source deposits trail there; nearby agents sense that trail and are drawn toward it too, creating a positive feedback loop that turns a single lucky path into a well-worn road, while paths nobody reinforces simply fade away as the field decays.

Why the network stays efficient, not just connected

A naive flood-fill would connect every food source too, but with a dense, wasteful tangle of paths. What makes the Physarum pattern interesting is that decay actively prunes redundant connections: a path that is only marginally shorter than an alternative accumulates trail slightly faster, wins more of the agent traffic, and the losing path decays away because nothing is reinforcing it anymore. The organism does not compute a shortest path in the graph-theoretic sense — it never sees the graph — but decay-versus-reinforcement acts as a distributed optimiser that converges toward something close to a minimum-cost tree, and it does so continuously and adaptively as food sources appear or disappear.

The Tokyo rail-network experiment

The most famous demonstration of this came from a 2010 study led by Atsushi Tero, published in Science. Researchers placed oat flakes — Physarum's preferred food — on a wet surface in the exact geographic layout of cities around Greater Tokyo, with the plasmodium starting at the position of central Tokyo. Over roughly a day, the slime mold grew a network connecting the oat flakes that closely mirrored the real Tokyo rail system: comparable total length, comparable transport efficiency, and comparable fault tolerance, meaning the network survived the simulated loss of individual links about as well as the real railway does. No engineer designed this network; it emerged from exactly the sense-turn-deposit loop described above, run on a substrate with no idea it was solving a transportation problem.

From biology to algorithm

Because the model is so cheap to simulate and produces organic, branching, fault-tolerant structures, the "Physarum algorithm" has been adopted well outside biology. It has been used to approximate solutions to network design and shortest-path problems, to generate procedural road and river networks in games and visualisation software, and as a physically-motivated alternative to more rigid graph algorithms whenever the goal is a network that degrades gracefully rather than one that is provably optimal but brittle. Its closest algorithmic relative is ant colony optimisation, which uses the same trail-based stigmergy but models discrete agents traversing a predefined graph rather than a continuous field — Physarum's version has no graph to begin with, it grows one.

Frequently asked questions

Try it live

Everything above runs in your browser — open Slime Mold Network (Physarum) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.