The Strange Computational Lives of Slime Molds

In 2010, a paper appeared in Science with one of the more arresting figures in the history of unconventional computing. The figure showed two side-by-side images. On the left, the railway network of greater Tokyo. On the right, a tube network grown by Physarum polycephalum, a slime mold, after thirty-six hours on an agar plate where oat flakes had been arranged at the locations of the major Tokyo train stations. The slime mold's network was, by quantitative measures of efficiency, robustness, and total tube length, a near-match for the engineered Tokyo network that thousands of human designers had refined over a century.

The slime mold did this with no brain, no nervous system, no central control of any kind. Physarum polycephalum is a single-celled organism. It is not a colony; it is not a multicellular animal; it is one enormous cell with millions of nuclei sharing a single cytoplasm. The thing it does, computationally, should not be possible by anything resembling the standard story of how computation arises in biology. It is doing the work in a substrate that the textbook narrative had retired a billion years ago.

What a slime mold is

Physarum polycephalum (the species most studied; there are several thousand others) is in a kingdom called Amoebozoa. It is not a fungus, despite the name and the moldy appearance. It is closer to an amoeba: a single-celled organism that, in its plasmodial stage, can grow to the size of a dinner plate while remaining one cell. The cytoplasm flows through tube-like channels called pseudopods, and the flow is rhythmic; the cell expands and contracts on a roughly two-minute cycle, with internal currents reversing direction in pulses.

The cell forages by extending pseudopods into the surrounding environment. When a pseudopod encounters food (typically bacteria or fungal spores in the wild, or oat flakes in the lab), it stays. When a pseudopod encounters nothing useful, it retracts. The cell as a whole optimizes its tube network over hours, thickening tubes that connect productive regions and abandoning tubes that lead to dead ends.

This is the mechanism. What turns the mechanism into computation is that the optimization, performed across millions of nuclei without any central coordinator, converges on solutions that are mathematically interesting.

The shortest-path problem

The most famous demonstration came in 2000, in a brief paper by Toshiyuki Nakagaki, Hiroyasu Yamada, and Ágota Tóth in Nature. They placed a slime mold in a maze, with food at the entrance and the exit. After several hours, the slime mold had filled the maze. After a day, it had retracted from the dead ends and concentrated its mass along the shortest path between the two food sources. The shortest path. Computed by an organism with no neurons, by a process that looks like a glorified protozoan extending pseudopods.

The mechanism, when worked out, is mathematically reasonable: thicker tubes carry more flow, more flow strengthens tubes (a positive feedback loop), and tubes with no flow gradually thin and disappear. The dynamics produce a tube network where the surviving tubes are the ones with the highest cumulative flow, which corresponds to the shortest path. It is essentially a continuous-time approximation to the kinds of relaxation algorithms used in numerical optimization. The algorithm was named the Physarum solver, and computer scientists have since shown that it converges in polynomial time on shortest-path and related problems.

Multi-source, multi-sink networks

The Tokyo result is more impressive than the maze result because it required the slime mold to balance multiple competing demands. Tokyo's actual rail network is not a single shortest path; it connects 36 major stations, and the optimization has to trade off total tube length, redundancy (alternative routes if one breaks), and average travel time. The slime mold produced a network that compares favorably with the human-designed network on all three metrics.

The 2010 paper, by Atsushi Tero and colleagues at Hokkaido University, was followed by similar experiments using slime molds to design networks for highways in the UK, motorway systems in Spain, the silk roads, and the structure of the Roman Empire's roads. In each case the slime mold's network correlated well with the engineered network. The pattern is robust enough that mathematicians have used it to propose adaptive network design algorithms for telecommunications networks, with the Tero results as the existence proof that the approach can work.

Habituation and memory

The 2016 paper by David Vogel, Romain Boisseau, and Audrey Dussutour at the University of Toulouse demonstrated something more unsettling: slime molds can be habituated. The team trained slime molds to cross a salt-coated bridge (slime molds find salt aversive). On the first crossing, the slime mold avoids the salt and takes hours to cross. On repeated exposures over days, the slime mold's avoidance fades; by the seventh trial, it crosses the salt bridge as quickly as a control bridge with no salt.

The habituation is specific to the trained substance: a slime mold habituated to salt is not habituated to caffeine, which is also aversive. The habituation persists across periods of dormancy: a slime mold trained to ignore salt, dried out into a sclerotium for a month, and rehydrated, retains the habituation. There is no neural substrate for this memory; the substrate is presumably some chemical or structural change in the cytoplasm, but the precise mechanism is not understood.

What is striking is the categorical question. If a single-celled organism can be trained, retain training across dormancy, and discriminate between aversive substances, the line between "computation" and "behavior" becomes harder to draw. The standard distinction between systems with memory (which need a brain or some equivalent) and systems without (which are simple chemistry) does not survive contact with Physarum.

What the slime mold is computing with

The substrate question is the deep one. Conventional computation uses transistors switching at gigahertz; brains use neurons firing at hertz to kilohertz. Slime molds compute with cytoplasmic flow on a timescale of minutes. The information-carrying primitives are the local thickness of the tube network, the local concentration of signaling molecules, the local rhythm of contraction.

The bandwidth is unimpressive, but the substrate has properties that conventional computers do not. It is fault-tolerant in a deep way; tearing the slime mold in half produces two slime molds, each of which retains some fraction of the trained behavior. It is energy-efficient; the slime mold solves shortest-path problems on millijoules of metabolic energy where a conventional computer would use kilojoules. It scales with the size of the problem in a way that does not require explicit programming; you give it food sources, it gives you a network.

The interest from computer scientists is not that we should replace silicon with slime mold. The interest is that the substrate exists, that it works, and that it suggests there are computational architectures we have not yet enumerated. Andrew Adamatzky's group at the University of the West of England has been the most prolific publisher in this space, with experiments demonstrating slime mold logic gates, slime mold distance estimators, slime mold approximate solutions to the traveling salesman problem.

What it means

The slime mold is a useful corrective to a particular kind of intellectual hubris about cognition. The story we tell about computation is that it requires a brain, which requires a nervous system, which requires multicellularity, which appeared in the Cambrian. Everything before that, the story goes, was just chemistry. The slime mold is a reminder that the story is wrong in detail and probably wrong in spirit. Single-celled organisms can do things that look very much like cognition, on substrates that predate the Cambrian by a billion years.

What the slime mold is doing is not human cognition, and there is no point pretending it is. It does not have a self-model, it does not plan, it does not represent its environment in a way that we can recognize as belief. But it solves problems, retains training, and discriminates. The space of cognitive-like processes in nature is much larger than the space of brain-having organisms, and the slime mold is one of the cleanest demonstrations of how big the difference is.

The next time someone tells you that intelligence requires a brain, the right response is to ask them what a slime mold is doing when it draws the rail network of Tokyo on an agar plate. Whatever the answer is, "nothing" is not it.