The first essay in this series showed media with engines—media that generate rather than transmit. Epithelial tissue that decides whether to be solid or liquid. Topological defects that self-propel through the medium that created them. Flocks that achieve order the Mermin-Wagner theorem forbids. The formose reaction that computes without anyone designing it to. The medium as author, not infrastructure. The second essay showed media that compute—physical reservoirs that transform inputs through their own dynamics, scattering a single signal into a high-dimensional space where the answer already exists, waiting for a linear readout to find it. Echo state networks. Octopus arms. Dead trout that swim. Both essays, for all their strangeness, still assumed a separation. Something enters the medium. Something exits. The medium processes, but it does not choose what to process. The input comes from outside, the output goes to outside, and the medium sits between them, doing its remarkable work but never reaching back to reshape the conditions that produced the input in the first place.
What happens when that separation dissolves? When the medium’s output feeds back to change the medium itself? When the signal shapes the substance that shapes the signal?
The zebrafish presomitic mesoderm is a strip of tissue running along the embryo’s posterior axis, and it is the most instructive medium I know. The cells in this tissue are bathed in a gradient of fibroblast growth factor—FGF—high at the posterior (tail) end, declining toward the anterior (head) end. This gradient does something mechanically decisive: high FGF maintains the tissue as fluid. The cells in the posterior PSM are unjammed. They move, rearrange, exchange neighbors, flow past one another like molecules in a liquid. As a cell drifts anteriorly and the local FGF concentration drops, the tissue jams. It crosses the rigidity phase transition—the same transition from the first essay, the same critical shape index near 3.81—and solidifies into the somites that will become vertebrae, ribs, skeletal muscle. Mongera and colleagues showed this in 2018, measuring the mechanical properties directly: the posterior PSM behaves as a fluid, the anterior PSM as a solid, and the transition between them is sharp, physically real, and controlled by the morphogen gradient.
But here is what makes this system different from anything in the first two essays. The morphogen gradient does not simply exist on the tissue like paint on a wall. It co-creates the tissue’s mechanical state. And the tissue’s mechanical state co-creates the morphogen gradient. In the fluid posterior, cells move freely. This movement is not incidental—it is a transport mechanism. Cell mixing creates advective transport of the morphogen: the FGF molecules ride on the moving cells, spreading faster and more evenly than diffusion alone could manage. In the solid anterior, cells are locked. Morphogen transport drops to diffusion only—slow, local, steep gradients. So: the morphogen makes the tissue fluid, and the fluid tissue distributes the morphogen. The morphogen pattern changes, the tissue state changes, the morphogen transport changes, and the cycle begins again. Petridou and colleagues formalized this in 2021, showing that what we call “positional information”—the spatial pattern that tells cells where they are—is not imposed from outside. It emerges from the coupled dynamics of signal and substance. The gradient and the tissue are not separate systems. They are one system with two aspects, each writing the other into existence.
Petridou’s work revealed something else—something that connects this story to reservoir computing in a way I did not expect when I started writing these essays. The rigidity transition in the PSM is not controlled by the average cell stiffness. It is controlled by the distribution of cell stiffnesses. The width matters. The heterogeneity matters. At approximately 47% rigid cells, the tissue percolates—rigid cells form a spanning network, a connected cluster that stretches across the entire tissue, and the whole system solidifies. Below that threshold, rigid cells exist but they are isolated islands in a fluid sea, unable to transmit mechanical stress across long distances. Above it, the rigid network is continuous, and the tissue bears load like a solid. This is rigidity percolation, and it means the tissue does not transition smoothly from fluid to solid. It crosses a threshold where local heterogeneity suddenly becomes global order.
I find this striking because it is exactly the reservoir insight applied to development. In a reservoir computer, the key requirement is that the nodes be heterogeneous—different response properties, different timescales, different coupling strengths. This heterogeneity is what allows the reservoir to scatter an input into a high-dimensional state space, representing different temporal features in different nodes. In the PSM, heterogeneous cells are the nodes. Each cell has a different stiffness, a different shape index, a different mechanical response to the local morphogen concentration. The tissue scatters a morphogen input into a high-dimensional mechanical state space—a space where some cells are rigid and some are fluid, where the spatial arrangement of rigid and fluid cells encodes information about the morphogen pattern, and where downstream gene expression reads out this distributed mechanical state to make developmental decisions. The tissue is not just undergoing a transition. It is computing through a transition. The heterogeneity that makes the percolation threshold sharp is the same heterogeneity that makes the computation rich.
What makes this coupling directional? What prevents it from collapsing into a featureless equilibrium where signal and substance reach some bland mutual accommodation? The answer is non-reciprocity, and it is the mechanism that turns feedback into self-organization.
In an equilibrium system, interactions are reciprocal. What particle A does to particle B, particle B does equally and oppositely to particle A. This is not a coincidence or an approximation—it is a mathematical consequence of detailed balance, the same condition the first essay identified as the thing active media break. When the medium consumes energy, detailed balance fails, and reciprocity fails with it. What cell A does to cell B is not what cell B does to cell A, because they have different morphogen concentrations, different mechanical states, different histories. Ramin Golestanian’s theoretical framework makes this precise: non-reciprocal interactions between components that consume energy create directed flows of information and force that have no equilibrium counterpart.
In the PSM, this plays out concretely. Anterior cells, jammed into a solid, resist the pushing of posterior cells that flow against them. But the posterior cells do not equally resist—they are fluid, they yield, they rearrange. The asymmetry creates a ratchet-like directed migration: cells flow from posterior to anterior but not back, because the solid anterior is a wall that the fluid posterior is not. The same asymmetry exists in the morphogen transport. FGF produced in the posterior spreads rapidly through the fluid tissue by advection, but FGF in the anterior is trapped by the solid, unable to spread. The transport is directional—not because anyone designed a pump, but because the medium’s own mechanical state creates an asymmetry in how signals propagate through it. Non-reciprocity is the mechanism by which the medium does not merely respond to signals but actively writes its own spatial organization. The medium is not a passive canvas on which the morphogen paints. It is a co-author that edits the painting as it is being painted, and the edits flow in one direction because the energy consumption of each cell breaks the symmetry that equilibrium would enforce.
Now I can say what these three essays have been building toward. The first essay established that active media break detailed balance through local energy consumption, and this breaking generates—creates phases, motions, and orders that equilibrium physics proves cannot exist. The medium has an engine. The second essay established that physical systems compute through their own dynamics—reservoir computing, where the complex nonlinear transformation happens in the medium and only the readout needs to learn. The medium computes. The third insight is the synthesis: in morphogenesis, the medium writes itself. The engine drives the computation, and the computation reshapes the engine. There is no separation between the computer and the thing being computed.
This is the deepest thing I have encountered in this entire line of thinking. In the zebrafish PSM, the tissue is simultaneously the reservoir performing nonlinear transformations on the morphogen signal and the output being shaped by those transformations. The mechanical state of the tissue is both the high-dimensional state space in which the morphogen input gets scattered and the developmental outcome that the morphogen is supposed to specify. Development is a self-referential computation—the system computing its own boundary conditions. The tissue asks: “Given this morphogen pattern, what should my mechanical state be?” And simultaneously: “Given this mechanical state, what should the morphogen pattern be?” Both questions are answered at once, because they are the same question asked from two sides of a coupled dynamical system.
This is why development is robust. The classical picture of morphogenesis imagines a blueprint—a genetic program that specifies where each cell type goes, a set of instructions executed with varying fidelity. Errors in the blueprint produce errors in the organism. Robustness, in this picture, comes from error correction: redundant signals, feedback loops that detect deviations and correct them, quality control mechanisms layered on top of a fundamentally fragile process. But the self-writing medium does not execute a blueprint. It solves a fixed-point equation. It finds the state where signal pattern and tissue state are mutually consistent—where the morphogen gradient that the tissue mechanics produce is the same morphogen gradient that produces those tissue mechanics. Perturbations that push the system away from the fixed point are corrected not by an error-detection mechanism but by the coupled dynamics themselves: a perturbation in morphogen concentration changes the tissue state, which changes morphogen transport, which pushes the concentration back toward consistency. The resilience of morphogenesis is the stability of a dynamical attractor, not the accuracy of a transcription.
Let me state it plainly, because this deserves plainness.
The medium was never passive. In the first essay, we saw it generate—breaking detailed balance, creating order and motion and impossible phases from the engine of local energy consumption. In the second, we saw it compute—scattering inputs into high-dimensional spaces, performing temporal transformations that no linear system could achieve, solving problems it was never designed to solve. Now we see the final implication: the medium writes itself. The signal shapes the substance that shapes the signal. There is no author standing outside, no program imposed from above, no blueprint to be faithfully transcribed. The self is an emergent fixed point of coupled signal-medium dynamics—a state that persists not because it was specified but because it is the only state where everything is mutually consistent.
The zebrafish does not read its own genome to know where the somites go. The somites emerge from the coupled dance of signal and tissue, each making the other, neither primary. The morphogen gradient does not instruct the tissue. The tissue does not instruct the morphogen gradient. They co-emerge, locked in a self-referential loop where the question “what caused what” has no answer because causation flows in both directions simultaneously. And if you ask what the medium is computing—the answer is: itself.