Morphogenesis: How Organisms Build Their Form
A human being begins as a single cell: one fertilized egg, roughly 100 micrometers in diameter, containing no visible structure that predicts the body it will become. Over the next nine months, that cell divides approximately forty trillion times. The resulting cells sort themselves — without any external direction, without any blueprint outside the cell itself — into 200 distinct cell types arranged in a precise three-dimensional architecture that is characteristic of the species.
How?
This is the problem of morphogenesis, and it is one of the deepest problems in biology. What makes it tractable — what gives researchers a formal language for thinking about it — is the observation that morphogenesis is, at its core, a computation. Each cell reads chemical signals from its neighbors, integrates that information according to rules encoded in its genome, and responds by dividing, differentiating, moving, or dying. The global form of the organism is the output of trillions of these local computations running in parallel. The cellular automaton is not an analogy for this process. It is a direct formal model of it.
The French Flag and the Positional Information Debate
Before the local-rule framework could be applied seriously to development, biologists had to settle a prior debate: does each cell know where it is?
The dominant paradigm in the 1960s said yes. Lewis Wolpert, at what was then the Middlesex Hospital Medical School in London, introduced the French flag problem in a 1969 paper in the Journal of Theoretical Biology: “Positional Information and the Spatial Pattern of Cellular Differentiation.” Imagine a row of cells that must become blue, white, or red in equal thirds, like the stripes of the French tricolor. Wolpert proposed that a chemical gradient — high concentration at one end, low at the other — provides each cell with a “positional value” encoding its location. Cells above threshold one become blue; cells between threshold one and two become white; cells below threshold two become red. The pattern is then a readout of position, not a self-organized phenomenon.
The French flag model is elegant and was widely adopted. It provided a framework for understanding how transplanted cells in classical embryology experiments could adopt fates appropriate to their new position. It implied a specific molecular prediction: there should be a morphogen gradient, diffusing from a source, that provides positional information.
The prediction was confirmed: Christiane Nüsslein-Volhard (who shared the 1995 Nobel Prize in Physiology or Medicine) identified Bicoid as the morphogen that provides anterior-posterior positional information in Drosophila embryos. The Bicoid protein diffuses from the anterior pole and decays exponentially; nuclei read the local Bicoid concentration and express genes accordingly. This is the French flag mechanism operating at the molecular level.
But Wolpert’s model leaves a question unanswered: where does the gradient come from? Who tells the anterior cell to secrete Bicoid, and how is that asymmetry itself established? The answer, in many developmental systems, is a Turing-type reaction-diffusion mechanism operating at an earlier stage. The positional information model and the self-organization model are not competitors — they operate in sequence. Self-organization generates an initial asymmetry; positional information is then read from the gradient that asymmetry produces.
The morphogenesis problem, properly stated, is not “positional information or self-organization?” but “at which stages is pattern generated by self-organization, and at which stages is pre-existing pattern read out?” The CA framework is essential for understanding the self-organization stages.
Lindenmayer Systems: Cellular Automata for Plants
In 1968, Aristid Lindenmayer, a biologist at the University of Utrecht, published a paper in the Journal of Theoretical Biology that introduced a formal language for describing plant growth. He was studying the development of algae — organisms with simple, linear filamentous structures — and he wanted a mathematical formalism that could describe the parallel development of all cells in the filament simultaneously.
His solution was an L-system: a formal grammar in which each symbol in a string represents a cell, and each generation the entire string is rewritten simultaneously according to production rules that replace each symbol with one or more symbols. The parallelism was essential to Lindenmayer’s biological intuition: cells in a developing organism do not take turns dividing. Every cell is computing simultaneously, and the rules each cell applies depend only on its current state, not on the global state of the organism.
This is a cellular automaton. The symbols are the cells. The production rules are the CA update rules. The string is a one-dimensional grid. The remarkable result — which Lindenmayer, Prusinkiewicz, and colleagues spent the following two decades elaborating in a series of beautiful papers and the 1990 book The Algorithmic Beauty of Plants — is that L-systems can generate representations of plant architecture of extraordinary fidelity. The branching structure of a fern, the spiral phyllotaxis of a sunflower, the iterative branching of a tree, the floral arrangements of mathematical precision found in nature: all are captured by L-system grammars in which every production rule applies only local information.
The CA parallel is explicit in the extension to parametric and context-sensitive L-systems, where the production rule for a cell can depend on the state of neighboring cells in the string. Context-sensitive L-systems are one-dimensional cellular automata with an L-system encoding for the cell states. They produce dynamics that resemble those of one-dimensional CA — pattern propagation, wave formation, stable attractors — in the developmental context.
The lesson is the same lesson Conway’s Life teaches: rich global structure from simple local rules. A tree is not complicated because its genome is complicated. It is complicated because simple iterative rules applied to a growing structure produce branching architectures of arbitrary depth.
Digital Morphogenesis: CA Models of Growth
The most direct CA approach to morphogenesis is to model developing tissue as a grid of cells, each updating its state according to rules that represent cell-cell signaling, and observe what global forms emerge.
Pioneering work by Hans Meinhardt — particularly in his 1982 book Models of Biological Pattern Formation — used reaction-diffusion simulations on two-dimensional grids to reproduce patterns from seashell pigmentation to the branching structure of blood vessels. Meinhardt was explicit about the connection between his continuous models and their discrete CA equivalents, and several chapters of his book are devoted to numerical simulations on grids that are, structurally, CA computations.
Coral growth provides a particularly clean example. Coral polyps grow at the surface of the coral structure, extending the structure by depositing calcium carbonate. Each polyp’s behavior depends on local signals from neighboring polyps: growth is activated in exposed regions and inhibited where the structure is already dense. The result — in both real corals and in CA simulations — is fractal branching architectures of great diversity. The branching pattern of Acropora staghorn coral, the plate-like form of Montipora, the brain-like folds of Diploria: these distinct forms can be reproduced by varying a small number of parameters in a CA simulation where cells grow outward according to activation-inhibition rules.
Developmental biologist Pere Alberch and theorist Stuart Newman used similar models in the 1980s to argue that the range of vertebrate limb shapes is determined not by an enormous number of genetic instructions but by the dynamics of a relatively simple reaction-diffusion system operating on a growing domain. The “developmental constraint” — the reason there are no six-fingered vertebrates in nature — is not primarily genetic but mathematical: the reaction-diffusion system on a limb domain simply does not produce stable six-peak solutions at the domain sizes and parameter ranges that vertebrate development actually uses.
Growing Neural Cellular Automata: Learning to Develop
The 2020 paper “Growing Neural Cellular Automata,” by Alexander Mordvintsev, Ettore Randazzo, Eyvind Niklasson, and Michael Levin, published in Distill on February 11, 2020, represents the most striking recent development at the intersection of CA and morphogenesis research.
The setup is simple to state. Each cell in a grid contains a small neural network — a compact function that takes the current state of the cell and its eight neighbors as input and produces an update to the cell’s state as output. The neural network parameters are shared across all cells (every cell runs the same network, just as every cell in a real organism contains the same genome). The network is trained by gradient descent: given a target image, optimize the network parameters so that starting from a single active cell, the system reliably grows to match the target.
The result is a system that learns to develop. Starting from a single cell, the trained network grows a coherent pattern that matches the target image. But the more remarkable result is robustness: when cells are deleted or the pattern is disrupted, the system regenerates. It does not simply restart development from scratch; it detects the damage and fills it in, converging to the correct final form from an intermediate state that was never in its training data.
This is morphogenesis in the full biological sense: a developmental process that produces a specific form and can recover from perturbations. And it is implemented as a cellular automaton: local rules, parallel update, no global coordinator.
Levin, who co-authored the paper and runs a research group at Tufts focused on bioelectric signaling in development, has argued that the growing neural CA captures something essential about real biological development: the goal-directedness. Biological organisms do not follow a rigid developmental script; they achieve a target form through feedback and correction. The growing neural CA demonstrates that this goal-directedness does not require any global intelligence or central controller — it can emerge from a local rule trained to reproduce a target output.
Xenobots: Programmed Morphogenesis in Living Cells
In January 2020 — the same year as the growing neural CA paper, a coincidence that itself says something about the maturation of the field — Kriegman, Blackiston, Levin, and Bongard published “A Scalable Pipeline for Designing Reconfigurable Organisms” in PNAS. The resulting organisms, named Xenobots after the African clawed frog Xenopus laevis from which they were made, were living biological entities whose form was designed computationally.
The design process used evolutionary algorithms running on the Deep Green supercomputer at the University of Vermont. Each candidate design was a configuration of two cell types — contractile heart muscle cells and structural skin cells — on a simple three-dimensional lattice. The fitness function was locomotion: designs that moved further were more fit. The evolutionary search explored the space of possible configurations and identified forms that exhibited efficient locomotion.
The winning designs were then physically assembled by microsurgery at Tufts: skin cells and heart muscle cells from Xenopus embryos were harvested, arranged in the computationally designed configuration, and allowed to self-organize. The resulting millimeter-scale organisms swam, navigated aqueous environments, pushed objects, and — in subsequent experiments — exhibited collective behavior including self-assembly from dispersed cells.
The Xenobots are relevant to morphogenesis for a specific reason: their behavior is not programmed into the cells. The cells are doing what frog cells always do — contracting if they are heart cells, providing structural support if they are skin cells. The intelligence, if you can call it that, is in the arrangement: the spatial configuration that the evolutionary algorithm discovered, which harnesses the normal behavior of the cells to produce locomotion. The whole is more than the sum of its parts, and the excess is a consequence of the spatial structure, not of any individual cell’s capability.
This is the CA principle expressed in living biology. The update rules are set by cell biology. The configuration is the design variable. The behavior is emergent.
Where the CA Analogy Breaks Down
The CA framework is a powerful tool for thinking about morphogenesis, but every tool has limits, and honest thinking requires naming them.
Cells are not identical. In a standard CA, every cell runs the same rule. In a developing organism, cells differentiate — they express different subsets of their genome at different times and in different locations, effectively running different rules. The CA model of development requires, at minimum, a multi-state CA where cells can switch between different rule sets as they differentiate.
The grid is deformable. Real developing tissue is not a rigid grid. Cells exert mechanical forces on each other; sheets of cells fold, invaginate, and migrate. The gastrulation process — the dramatic rearrangement of cell sheets in early embryos — cannot be captured by a CA on a fixed lattice. It requires a model in which the grid geometry itself changes as a function of cell behavior.
Cells move. In a standard CA, cells stay in their grid position. In real development, cells migrate — sometimes over substantial distances. Neural crest cells, for example, depart from the developing neural tube and migrate to form diverse structures including the peripheral nervous system, the pigment cells of the skin (relevant to Turing patterns), and the cartilage and bone of the face.
The rules evolve. In a standard CA, the rules are fixed. In biological evolution, the rules — the gene regulatory networks that specify cell behavior — are subject to mutation and selection. Modeling evolutionary morphogenesis requires treating the CA rule as a variable that changes across generations.
These limitations do not invalidate the CA framework for morphogenesis; they identify where it needs to be extended. The extensions — multi-state CA on deformable grids with mobile agents and evolvable rules — are active research areas, and the formal tools developed for simple CA transfer, often with modification, to the more complex models. The Game of Life may be a simplification. But it taught us what questions to ask.