An interactive laboratory for cellular automata and agent-based models.
Open the lab → · Read the paper (PDF) →
Ten models, from Wolfram's elementary rules to a nutrient-limited bacterial colony, each with the parameters its authors used and the citation it came from. The simulation cores are C, compiled to WebAssembly. Everything the models measure — population, entropy, fractal dimension, Gini coefficient — is computed live and plotted next to the grid, because a simulation you cannot measure is a screensaver.
The thread running through the ten is a single question: how does something alive — a bacterial colony, an ecosystem, a society — find food, survive, adapt, and organise itself, when nothing in it can see further than its own neighbours?
| Model | The point | |
|---|---|---|
| ★ | Bacterial colony | A nutrient field, and cells that eat it. Starve the colony and it branches into a fractal of dimension ≈1.7. Feed it and it fills in as a disc of dimension 2. Nothing about the cells changed. |
| ★ | Gray–Scott | Two chemicals, no biology, and spots that divide like cells. |
| ★ | Lenia | Conway's Life with every discrete thing about it dissolved. Something survives the dissolution, and it swims. |
| ★ | Cyclic competition | Rock, paper, scissors on a lattice. Whether all three species survive is decided by one number: how far they wander. |
| ★ | Sugarscape | A scrupulously fair world. Watch the Gini coefficient climb to 0.5. |
| Segregation | Nobody in this model is a segregationist. The city segregates anyway. | |
| Life-like | Not the Game of Life — all 262,144 of them, in one branchless kernel. | |
| Elementary CA | Eight bits of rule. One of them is a universal computer. | |
| Langton's ant | Ten thousand steps of chaos, and then, for no reason anyone can state, a road. | |
| Forest fire | Why the world is full of power laws, when criticality is supposed to be a knife-edge nothing can balance on. |
Each model has a panel with the rule stated plainly, three or four try this recipes that take you straight to the regime worth seeing, and the reference it came out of.
It measures. Every model streams observables into a common bus, plotted live. The bacterial colony's box-counting dimension is the one to watch: starve the colony and you can see D walk down from 2.0 towards 1.71 — which is the value Witten and Sander derived in 1981 for diffusion-limited aggregation, from an argument about random walkers that has nothing to do with biology, and the value Fujikawa and Matsushita measured in 1989 on an actual plate of Bacillus subtilis. Watching a simulation converge on a number somebody else got out of a Petri dish is a different experience from watching a pretty pattern.
It is reproducible. Every run is a pure function of its seed and its parameters, and all of them live in the address bar. Copy the link and you are not sharing a picture of a run — you are sharing the run, cell for cell. The generators are PCG32, seeded per stream; no wall-clock ever enters an update; the speed control changes how many generations happen per frame and never what happens in one.
It sweeps. Each model carries a reproduce the figure button. Press it and a pool of Web Workers runs the model a hundred-odd times across a parameter range — headlessly, in parallel, each worker with its own WebAssembly instance — and draws the phase diagram as the points come back. Schelling's segregation curve takes about four seconds. Orbium's survival map in the (μ, σ) plane, which is 168 independent runs of a convolutional field, takes about forty, and what it draws is a thin diagonal filament: the region in which the creature is alive rather than evaporated or cancerous. You do not have to take anybody's word for the edge of chaos. You can watch it get measured.
It is answerable to the literature. These are not tolerances invented to make the tests pass. They are numbers other people measured, and if the code stops reproducing them then the code is wrong:
| Check | Expected | Source |
|---|---|---|
| Starved colony, box dimension | fractal, D → ~1.7 | Witten & Sander 1981; Fujikawa & Matsushita 1989 |
| Fed colony, box dimension | compact, D = 2.0 | — |
| Rule 90 from one live cell | Sierpiński triangle, D = log3/log2 = 1.585 | Wolfram 1983 |
| Conway's Life from random soup | ash density ≈ 0.03 | — |
| A glider, after 64 generations | still five cells | — |
| Sugarscape, from equal endowments | Gini ≈ 0.4–0.5 | Epstein & Axtell 1996 |
| Schelling at τ = 0.35 | segregation ≈ 0.77, from a chance baseline of 0.50 | Schelling 1971 |
| Orbium, 400 steps | alive, mass bounded and nonzero | Chan 2019 |
| Orbium with σ = 0.005 | dead | Chan 2019 |
| Rock–paper–scissors, high mobility | at least one species extinct | Reichenbach et al. 2007 |
| Forest fire | self-organises to a critical density | Drossel & Schwabl 1992 |
make test runs all of them natively, and so does CI on every push.
morphogen: a browser-native laboratory for cellular automata and agent-based models — the write-up, in the form it wants to be in: the architecture, the measurements, the validation against the literature, and a section on the things that did not work.
(That link is the copy served from the site, because GitHub's own PDF viewer
gives up on this file often enough to be annoying. The same file is in
paper/ if you would rather have it from the repository.)
Every number and every figure in it is generated by tools/figures.c, which links
against the same src/core the browser runs. There is no separate figure code
that could quietly drift away from the thing being described: if a plot in the
paper is wrong, the simulation is wrong. make paper rebuilds it from scratch.
The most useful section is probably the one on negative results. The first version of the colony model let its cells wander freely, produced a diffuse cloud that was nothing like a colony, and box-counted to D ≈ 1.71 — right on the Witten–Sander value, and completely wrong. A scattered point cloud is fractal too. The test passed and the physics was absent, which is worth knowing about any growth model validated on a single scalar.
src/core/ is portable C99 and has no Emscripten dependency, so the same
simulation code compiles with the system compiler and runs outside the browser.
That is the point of the layout: the models can be profiled with real tools and
checked against the literature without a browser anywhere in the loop, and
WebAssembly is just one more target.
make test # build the core natively and check it against the literature
make # build the wasm module and assemble dist/
make serve # and serve it on :8000Building the wasm needs Emscripten. The built module is
committed to dist/, so if you only want to run the thing or work on the
interface, python3 -m http.server inside dist/ is enough and you need no
toolchain at all.
src/core/ the science. C99, no dependencies.
rng.h pcg32, and a counter-based hash for order-independent randomness
field.c halo-free neighbour tables and the shared diffusion kernel
obs.c entropy, box-counting dimension, Gini, segregation
model.h the interface all ten models implement
models/ one file per model, each with its rule and its citation at the top
src/wasm/api.c ~12 exported symbols. The boundary is crossed three times a frame.
src/web/ the interface. No framework, no bundler, no dependencies.
js/halftone.js the renderer: a WebGL2 halftone screen, one per ink
tests/main.c the literature, as assertions
The renderer prints rather than draws. Each model exposes up to four ink channels, and each is rendered as its own halftone screen — a lattice of dots whose radius encodes the value — laid down at its own screen angle. That last part is not decoration: printing two screens at the same angle collides them into a moiré, so a press rotates them apart and the dots interleave into a rosette instead. Cyclic competition has three species and prints as three separations. Dot radius goes as the square root of the value, because a dot's optical density is proportional to its area, and a linear mapping crushes the midtones into mud.
The simulation never copies a pixel. C owns an ink buffer inside the
WebAssembly heap; JavaScript takes a typed-array view straight into it and hands
that to the GPU. The only copy in the pipeline is the driver's upload to VRAM.
Memory growth is switched off, deliberately: a memory.grow silently detaches
every typed-array view held into linear memory, including that one, and the
symptom is a blank canvas with no error anywhere. Allocating once removes the
failure mode instead of papering over it.
Two things in here are easy to get wrong, and I got both wrong first. Lenia's Orbium was found under the polynomial kernel and growth function, not the exponential ones the paper writes down; load it under the exponential core and the creature does not glide, it wobbles and dies (the lab offers both, so you can watch that happen). And in the forest fire, treating every cell burning anywhere on the map at a given moment as one fire — the obvious shortcut — silently destroys the power law, because in the critical regime two fires are almost always burning somewhere at once, so the counter never closes and fifteen hundred generations report a single enormous fire. Each fire is numbered.
The full citation for each model is in the panel, in the source file, and here.
- Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Czirók, A. & Vicsek, T. "Generic modelling of cooperative growth patterns in bacterial colonies." Nature 368, 46–49 (1994).
- Witten, T. A. & Sander, L. M. "Diffusion-limited aggregation, a kinetic critical phenomenon." Phys. Rev. Lett. 47, 1400–1403 (1981).
- Fujikawa, H. & Matsushita, M. "Fractal growth of Bacillus subtilis on agar plates." J. Phys. Soc. Jpn. 58, 3875–3878 (1989).
- Pearson, J. E. "Complex patterns in a simple system." Science 261, 189–192 (1993).
- Turing, A. M. "The chemical basis of morphogenesis." Phil. Trans. R. Soc. B 237, 37–72 (1952).
- Chan, B. W.-C. "Lenia — Biology of Artificial Life." Complex Systems 28(3), 251–286 (2019). arXiv:1812.05433.
- Reichenbach, T., Mobilia, M. & Frey, E. "Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games." Nature 448, 1046–1049 (2007).
- Kerr, B., Riley, M. A., Feldman, M. W. & Bohannan, B. J. M. "Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors." Nature 418, 171–174 (2002).
- Epstein, J. M. & Axtell, R. Growing Artificial Societies: Social Science from the Bottom Up. Brookings / MIT Press (1996).
- Schelling, T. C. "Dynamic models of segregation." J. Mathematical Sociology 1(2), 143–186 (1971).
- Gardner, M. "Mathematical Games: The fantastic combinations of John Conway's new solitaire game 'life'." Scientific American 223(4), 120–123 (1970).
- Wolfram, S. "Statistical mechanics of cellular automata." Rev. Mod. Phys. 55, 601–644 (1983).
- Cook, M. "Universality in Elementary Cellular Automata." Complex Systems 15, 1–40 (2004).
- Wuensche, A. "Classifying cellular automata automatically." Complexity 4(3), 47–66 (1999).
- Langton, C. G. "Studying artificial life with cellular automata." Physica D 22, 120–149 (1986).
- Drossel, B. & Schwabl, F. "Self-organized critical forest-fire model." Phys. Rev. Lett. 69, 1629–1632 (1992).
- Bak, P., Tang, C. & Wiesenfeld, K. "Self-organized criticality: An explanation of 1/f noise." Phys. Rev. Lett. 59, 381–384 (1987).
- Clauset, A., Shalizi, C. R. & Newman, M. E. J. "Power-law distributions in empirical data." SIAM Review 51, 661–703 (2009).
MIT. The Orbium seed data is transcribed from Bert Chan's Lenia species list (MIT).