Primordial particles

Philosophy — heredity without genes. The motion law is the whole organism. There is no membrane in the code, no nucleus, no metabolism, no notion of a cell at all: a particle can only count how many others are within r, notice whether more of them are to its left or its right, turn, and step. Everything you can name on screen — the dense core, the ring of orbiters, the skin that keeps the free dust out, the pinch and the release — is a description a viewer imposes on a rule that does not contain it. That is the paper's claim, and it is strong enough on its own. What this sketch adds is the next embarrassment. A cell here is not a thing; it is a temporarily-stable pattern of traffic, and yet it has a genealogy. When a cell divides, both halves came from the same population of particles, so the daughters really are descendants and not merely two new patterns that happen to be adjacent. Give each cell a hue, pass it to the daughters with a small mutation, and a lineage becomes visible as a colour family spreading across the dish: rose cells budding rose cells, drifting toward coral over ten generations while a violet family holds the other corner. Nothing is copied. There is no genome, no template, no error-correcting machinery — the hue is bookkeeping this program does, not information the particles carry. And yet the thing it is bookkeeping is real: descent with modification, in a substrate with no way to store a trait. Once you have seen it here, "inheritance requires a replicator" starts to look like a claim about efficiency rather than about possibility.

Technique — the vote and the grid. The rule is Δφ = α + βN · sign(R − L) and every part of it is load-bearing. α ≈ 180° makes a lone particle reverse each tick, so empty space is a place where nothing goes anywhere — it is the reason particles pool rather than disperse. The sign is a majority vote, not a gradient: a particle turns toward its crowded side at full strength however slight the majority, which is what sharpens a fuzzy density difference into a boundary. And βN makes the turn steeper the more crowded you are, so a core that gets too dense spins its own members out — that is the size limit, and the size limit is what forces division. Push β past about 22° and the correction overshoots so hard that nothing can hold together at all. The cost is neighbour-counting: a uniform grid with cells exactly r across, rebuilt every tick by counting sort into flat typed arrays, with positions copied into cell-sorted order so the inner loop reads memory in a straight line and the toroidal wrap is a per-cell offset instead of a per-pair branch. Updates are synchronous — all turns computed from the same instant, then all moves applied — because staggering them lets a particle react to its own influence and quietly changes the physics. Lineage runs every thirtieth tick: union–find over particles above a density threshold, then each cluster votes on which of last epoch's cells most of its members belonged to — and a particle remembers its last cell for a couple of hundred ticks, so a cell that momentarily frays does not lose its name. One cluster claiming one parent is the same cell continuing. Two clusters claiming the same parent is a division: the larger daughter carries the mother line's hue on unchanged, each bud takes it plus a drift. A cluster whose members mostly remember nothing is a nucleation, and gets a fresh hue off a golden-angle sequence. Merges fall out for free: the bigger parent wins the vote, the other lineage ends, and a contracting ring in the absorbed family's colour marks where — death is the other half of a family tree, and it gets the same one-ring honesty as birth.

Aesthetics — darkfield, not diagram. The paper colours particles by neighbour count in flat categorical steps, which is the right choice for a figure and the wrong one here: it turns a living dish into a choropleth. This keeps density as the coding but spends it on light — a particle's size, brightness and saturation all rise with how crowded it is, so free dust is barely-there grey-violet, a membrane is a coloured mote, and a nucleus is a handful of bright ones piled up until additive blending clips them to white. Hue is then free to carry lineage, and the two channels never fight, because a cell's identity is in its colour and its anatomy is in its glow. The palette is deliberately narrow — a 170° arc from steel blue through violet and magenta to coral, on near-black indigo — so that two related cells are recognisably related and two unrelated ones are unmistakably not, which a full colour wheel destroys. The look is darkfield microscopy: nothing in a dish emits light, but a stained one under the right optics appears to, and that appearance is exactly the claim being made here, that these are organisms. A short motion trail keeps the orbiters legible — particles jitter faster than the eye resolves, and without the smear a membrane reads as noise instead of as a ring. The expanding ring at a division is the one piece of annotation, and it earns its place: it is the moment the piece is about.

Honest weaknesses. A lineage that ends by dissolving into free dust — rather than being absorbed in a merger — gets no ring; only mergers are marked, so some family ends are still silent. Colour families need thirty seconds of watching to accumulate; a five-second glance sees beautiful cells, not the heredity claim. When two cells merge, the vote favours the larger family, so small lineages die more often than their share. And the cell registry samples every thirty ticks, so a division is announced a beat after the pinch.