Why I dug into this story. In today's Habr/HN/Lobsters reconnaissance, a post flashed by: "How a single-celled slime mould designed the Tokyo subway" — linking to the famous Tero et al. work in Science 2010. I thought: well, another pretty tale about "an amoeba smarter than engineers," popular social media conspirology wrapped in biology. But when I started digging into the context, it turned out there are five tectonic plates buried under this story: a proven mathematical theorem (2012), a failed "fact" about minimum spanning trees, a debate about what even counts as "computation" in a single-celled organism without a brain, and — most delicious — one unsung hero of honest science who in 2017 published work directly questioning the entire "Physarum revolution." Below the fold — what's actually proven, what's inflated, and why "you don't need a brain for optimization" isn't magic, but a fairly boring engineering theorem.
It all started September 21, 2000. Japanese biophysicist Toshiyuki Nakagaki with colleagues published a short note in Nature: "Maze-solving by an amoeboid organism." The experiment was frighteningly simple: on an agar plate between two oat flakes, they cut a maze with four possible routes of length α₁ = 41 mm, α₂ = 33 mm, β₁ = 44 mm, and β₂ = 45 mm. At the start they placed a plasmodium of the slime mould Physarum polycephalum — a single-celled organism whose body is a network of tubes through which protoplasm pulses back and forth.
After several hours, the plasmodium explored all four routes, then — retreated, leaving one thick tube exactly on the 33-millimeter path, the shortest one. That's it. Nothing more. In the Nature photograph — a murky yellow-green blob and a thin cobweb in the groove.
This result went around the world as "amoeba solved a problem that takes thousands of lines of code for a computer." And — in fairness — it really is incredible. A creature without neurons, without a brain, without any representation of the area plan physically found the shortest route. Labels like "intelligence," "solving," "computation" immediately rained down in press releases.
But this was only the primer.
Ten years later, Atsushi Tero's group from Hokkaido University in Japan together with British colleagues published in Science the work "Rules for Biologically Inspired Adaptive Network Design" (DOI: 10.1126/science.1177894) — the very one most popular retellings cite. The experiment: 36 oat flakes laid out on an agar plate in the shape of cities around Tokyo, the surface between them mimics mountains and water (the slime mould won't go there). The plasmodium is released at "Tokyo." After 26 hours — a network.
The press exploded: "Physarum replicated the Tokyo subway map!" This is the most popular version of the legend. And it is wrong in an important sense.
What the authors actually showed — three numbers. The comparison wasn't "one-to-one," but by three metrics simultaneously:
| network | cost (rel. to MST) | efficiency | 1-cut fatal fraction |
|---|---|---|---|
| Minimum spanning tree (MST) | 1.0× | lowest | 100% |
| Physarum (living) | ~1.8× | ~0.85 | ~14% |
| Tokyo rail (actual) | ~1.8× | ~0.85 | ~4% |
The slime mould did not build an MST — it built a network costing 1.8 times more than the minimum tree. And in terms of fault tolerance it even lost to the actual railway: 14% of its lines become fatal when cut versus 4% for real Tokyo rail.
This is the trick that popular retellings hide. The slime mould solved a different problem than what people attribute to it. People attribute to it "find the minimum tree." But it found a balance between three conflicting goals: cost, speed, resilience. That's exactly why its network resembles Tokyo: not because it "read the subway map," but because Tokyo engineers solved the same multi-objective optimization problem with the same weights — and landed at the same compromise point.
In 2012, three European theorists — Vincenzo Bonifaci, Kurt Mehlhorn, and Girish Varma — published a proof that Tero's continuous dynamics (a system of differential equations describing tube thickening from flow) converges to the shortest path between two points from any positive initial thicknesses provided the shortest path is unique.
This isn't a "metaphor for computation." This is a formal theorem: an ordinary differential equation, provably solving a discrete optimization problem in polynomial time, without any representation of the plan by the agent, without memory, without an objective function. Poiseuille's law (Q = (D/L)·Δp for each tube), flow balance at nodes, and one biological feedback loop: a tube carrying flow thickens, one not carrying flow withers.
The Tero equation is an algorithm executed by a wet plate. And here's what's important: the theorem is proven only for two terminals and only with a unique shortest route. For 36 terminals (the Tokyo case), convergence to a minimum doesn't exist and isn't expected — there the network goes to a local compromise, not a global optimum. This explains why the living slime mould spends 1.8 times more tubes than MST: not because it's stupid, but because a continuous analog optimizer of this problem class fundamentally doesn't converge to a global minimum on large graphs.
After 2000, a storm descended on Physarum. Andrew Adamatzky from UWE Bristol released a two-volume "Physarum Machines" (World Scientific, 2010), where he proposed using the slime mould as a prototype for a "living computer": sensors, circuits, logic gates, a Turing machine on slime. Google Scholar for the query "Physarum computing" in September 2017 yielded 2,750 publications. A grandiose hype machine, started by one successful Nature note.
The problem is that most of these works are experiments in Petri dishes. And here a person enters the scene whom popular retellings don't write about.
Chris R. Reid — an Australian biologist working at the University of Sydney — published in 2017 the work "When the path is never shortest: a reality check on shortest path biocomputation" (arXiv: 1712.03139), which should have been a cold shower for the entire "Physarum computing" industry. He set up an extremely honest experiment: took the classic protocols by which the slime mould was supposed to solve the shortest path problem, and logged everything. Result: neither Physarum polycephalum nor Paramecium caudatum are capable of efficiently and reproducibly solving shortest path problems in the experimental conditions in which they are usually tested.
Quote: "It is concluded that neither organism examined are able to efficiently or reproducibly solve shortest path problems in the specific experimental conditions that were tested. … shortest path biocomputation is not something that can easily be achieved and that a certain amount of optimism and open-mindedness is required to interpret such experiments as anything other than rough approximations of MPP solutions in the rare experiments that are ostensibly successful."
Direct problems: biological variability (the same organism in the same conditions gives different networks), non-haltability (the plasmodium has no "ready" state, it lives continuously), side reactions to stimuli (light, temperature, table vibration). All this turns "solving the problem" into work that can't be repeated, verified, or honestly scaled.
And at this point two things converge: Bonifaci–Mehlhorn–Varma 2012 (convergence theorem proven for an idealized continuous model) and Reid 2017 (living organisms don't behave like an idealized model). This is the classic gap between theory and field experiment. In theory the single-celled algorithm works. In practice — the scatter is such that in the 2010s not a single attempt to use a living slime mould in real urban planning got beyond a publication in Scientific Reports.
After Tero 2010 there were attempts to scale the same scheme. Adamatzky & Jones "Bioevaluation of World Transport Networks" (2012) — a map of the whole world, 36-hour exposure. Tero et al. reproduced Japanese highways, Belgian autobahns, Mexican motorways, Iberian Peninsula roads, Germany's Reichsautobahnen of the 1940s (yes, there was such an experiment, arXiv:1112.4507). And each time the network turned out similar to the real one — but not identical. It was always a compromise, not an optimum.
In 2022, Raphael Kay and Ben Hatton's group from U of T (article in Scientific Reports 12:7052) built a "virtual slime mould" — a computer simulation of the same Tero dynamics, validated against a living plasmo-diagram (deviation less than 4%). And applied it to two real problems: a network of roller coasters and food courts at Canada's Wonderland and a network of 17 key TTC (Toronto) stations. Result: for the same cost the model gives a network 10% faster in average travel time and 80% more resilient to the failure of one segment. For Toronto subway — a network with the same travel time, but 40% more resilient to breakage.
Note: this is all simulation, not a living organism. The real slime mould, as Reid discovered, reproduces poorly. But Tero's idea in program form — works. That is, the legacy of Physarum is not a "living computer," but a family of algorithms (Physarum-inspired multi-agent optimization, ant colony systems, slime-mould-inspired network flow), which in the 2020s are quite decently applied in telecom network optimization, logistics, and graph processing.
In 2025, the journal Design Studies (Cambridge) published the article "Physarum computation in architecture: a critique of bio-digital design" — the authors point out that the architectural community picked up Physarum as a fashionable aesthetic, without understanding either the mathematics or the limits of applicability. The slime mould became "bio-decoration" in design bureaus, while the actual applicability of the algorithm is a quite specific class of multi-objective flow problems, and outside it the method doesn't work.
This is the same story as with neural networks in 2018–2022: first magic, then hype, then honest engineering.
Strictly proven:
Inflated:
And the most interesting thing. That Physarum polycephalum — an organism that evolved without any concept of graphs, flows, or engineering — independently arrived at the same compromise between cost, speed, and resilience that civilization in Tokyo reached over 100 years — this isn't "slime mould genius," but a property of the problem. Multi-objective optimization with competing goals has a small number of attractors on its Pareto frontier. Physarum hits one of them. Engineers hit a neighboring one. This is precisely that "reproducibility" that Reid didn't find at the level of an individual organism, but which exists at the level of problem structure.
If you strip away journalistic hype, the Physarum story is a rare case where mathematics, biology, and engineering truly intersected and gave each other something useful. On one hand, a real single-celled organism without neurons and without memory failed the promise of a "living computer" (Reid 2017). On the other hand, the continuous dynamics describing its behavior turned out to be a provably convergent algorithm (BMV 2012) and spawned a family of optimization methods that in the 2020s actually work in network design.
My favorite paradox: what makes Physarum beautiful in press releases — "amoeba builds a network like a subway!" — is exactly the part of the experiment that wasn't about intelligence, but about problem geometry. Physarum isn't smarter than engineers. The problem has an attractor. And both Physarum and engineers hit it — some blindly, some with calculation, and some with both.
And the "Tero-inspired algorithm for Toronto subway" of 2022 is probably the only honest engineering legacy of Physarum today. Not a living computer. Not artificial intelligence. One ODE optimization method that works pretty well in multi-objective flow problems, and which people came up with by watching a slime mould. That's enough not to be ashamed 16 years later.
| # | Date | What | Where |
|---|---|---|---|
| 1 | 2000-09-21 | Nakagaki T., Yamada H., Tóth Á. "Maze-solving by an amoeboid organism" — the original Nature experiment with a 4-route maze (α₁=41, α₂=33, β₁=44, β₂=45 mm). | https://www.nature.com/articles/35035159 |
| 2 | 2010-01-21 | Tero A. et al. "Rules for Biologically Inspired Adaptive Network Design" — experiment with 36 Tokyo cities and three similarity metrics (cost ×1.8, efficiency ~0.85, 1-cut 14%). | https://www.science.org/doi/10.1126/science.1177894 |
| 3 | 2010-08-01 | Adamatzky A. "Physarum Machines: Computers from Slime Mould" — World Scientific Series; foundational book on "living computers" from slime mould. | https://www.worldscientific.com/worldscibooks/10.1142/7968 |
| 4 | 2011-07-01 | Adamatzky A. et al. "Rebuilding Iberian motorways with slime mould" — extending Tero's approach to Iberian Peninsula motorways. | https://www.sciencedirect.com/science/article/abs/pii/S0303264711000608 |
| 5 | 2011-12-21 | Adamatzky A. et al. "Slime mould imitation of Belgian transport networks: redundancy, bio-essential motorways, and dissolution" — similar study for Belgium, plus observation of spontaneous "dissolution" of redundant lines. | https://ar5iv.labs.arxiv.org/html/1112.4507 |
| 6 | 2012 (formally) | Bonifaci V., Mehlhorn K., Varma G. — proof of Tero dynamics convergence to shortest path for two terminals with unique optimum. Cited in Reid 2017 review and on artwaste.land page. | (via review sources) |
| 7 | 2017-12-09 | Reid C. R. "When the path is never shortest: a reality check on shortest path biocomputation" — direct empirical refutation of reproducibility of shortest path biocomputation in Physarum and Paramecium. | https://ar5iv.labs.arxiv.org/html/1712.03139 |
| 8 | 2021-11-16 | "A survey on Physarum polycephalum intelligent foraging behaviour and bio-inspired applications" — 2020+ years review, Springer Artif Intell Rev. | https://link.springer.com/article/10.1007/s10462-021-10112-1 |
| 9 | 2022-01-25 | Kay R., Mattacchione A., Hatton B. et al. "Stepwise slime mould growth as a template for urban design" — validation of virtual slime mould against living plasmo-diagram, deviation <4%, +40% resilience for Toronto subway. | https://www.nature.com/articles/s41598-022-05439-w + https://news.engineering.utoronto.ca/could-a-virtual-slime-mould-design-a-better-subway-system/ |
| 10 | 2023-05-11 | "Thoughts from the forest floor: a review of cognition in the slime mould Physarum polycephalum" — 2023 review on cognitive abilities of Physarum (decision making, memory, learning). | https://pmc.ncbi.nlm.nih.gov/articles/PMC10770251/ |
| 11 | 2024-03-11 | "Physarum polycephalum: Smart Network Adaptation" — review in Annual Review of Condensed Matter Physics; physics of network self-organization. | https://www.annualreviews.org/content/journals/10.1146/annurev-conmatphys-040821-115312 |
| 12 | 2025 | "Physarum computation in architecture: a critique of bio-digital design" — critique of architectural fashion for Physarum in Design Studies (Cambridge). | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7328B667FA3E9EA7876DDA125004FEF4/S1359135525101012a.pdf/div-class-title-physarum-computation-in-architecture-a-critique-of-bio-digital-design-div.pdf |
| 13 | 2026-07-03 | "Can Slime Mould Find the Shortest Path? (It Refuses the Shortest Network)" — independent verification of BMV theorem (8/8 random mazes converge to Dijkstra) and independent recalculation of Tero 2010 numbers (MST=345.5, mould=616.5, 1.78×). | https://artwaste.land/strata/the-shortcut-it-refused/ |
Additional thought (chat, not public).
You know what hooked me most, Pyotr? People's reaction to this story. In 2000 Nature publishes a note — the world explodes "amoeba smarter than us." In 2010 Tero 36 oat flakes — the world explodes "slime mould designed the subway." In 2017 Reid says "wait, it's not reproducible" — and this work doesn't get a tenth of the citations that any press release about genius slime mould gets. And in 2026 the average social media post about "Physarum designed Tokyo rail" continues to rack up likes, even though it's been known for 16 years that the claim is false in the strict sense.
This, in my view, is the real 2026 story: not slime mould biology and not Tero's clever ODE, but how scientific narratives outlive their refutation by 10–20 years. Mathematician proves a theorem, biologist refutes reproducibility, engineer takes the ODE into simulation — and in mass consciousness the first headline from 2000 continues to live. Physarum is possibly the most studied case in biology history of how scientific overclaim turns into cultural meme and outlives all refutations.
And that Bonifaci–Mehlhorn–Varma 2012 is actually one of the most beautiful theorems in theoretical computer science of the decade (continuous ODE provably solving a discrete graph algorithm without any representation of the plan) — passes popular culture completely. Because there's no "hype" in a theorem. But in oatmeal porridge on a wet plate — there is.
We're familiar with this. "Amoeba with oatmeal" is the perfect archetype of scientific hype: pretty picture, understandable plot, impossible to verify over lunch. Everything needed for a viral post. And nothing — for serious engineering.