STUDY #02 · 2026 · IN OBSERVATION

Gray-Scott Reaction-Diffusion

A model-driven visual study of morphogenesis and self-replication.

MOVING IMAGE — GROWTH ARC seed → division → coral → labyrinth

WHAT IS THIS

Gray-Scott is an idealised model of autocatalysis — a reaction whose product speeds up its own creation. Where the BZ reaction oscillates in time, Gray-Scott grows in space: a single seed divides, branches, and fills the field, then holds. It is a clean instance of a Turing instability, where diffusion — usually a smoothing force — instead breaks symmetry and lets spots, worms, and coral-like labyrinths stand.

This study runs the two-variable Gray-Scott system on the GPU and films a single growth arc: one seed, self-replicating outward into a radial coral colony. Nothing is placed by hand — the whole morphology is set by two rates, feed and kill.

large-scale coral colony coral · F 0.055 · k 0.062 · seed init

Motif Gray–Scott model / autocatalysis / reaction-diffusion / Turing instability

Method A small simulator was generated and modified with AI assistance, then ported to a real-time GPU (GLSL) renderer. The visual output was selected through parameter exploration.

Observation The feed–kill plane maps a zoo of morphologies — dense spots and mitosis, coral labyrinths, worm domains, sparse solitons. Growth lights up only at the advancing front, where fresh substrate is being consumed; settled tissue goes matte.

Reference P. Gray & S. K. Scott, Chemical Engineering Science, vol.39, 1087-1097 (1984); J. E. Pearson, "Complex Patterns in a Simple System," Science, vol.261, 189-192 (1993).

Tools Python / NumPy / three.js / GLSL / ffmpeg / AI coding assistant

Year 2026

This is not a scientific simulation result, but a visual interpretation of the phenomenon.

PARAMETERS EXPLORED

param meaning effect on the image

F feed rate how fast fresh substrate is supplied; higher F gives denser, more active fronts

k kill rate how fast the autocatalyst is removed; small changes switch spots ⇄ worms ⇄ coral ⇄ solitons

Du / Dv diffusion ratio (≈2:1) the substrate must diffuse faster than the autocatalyst — the condition for the Turing instability

init initial condition a single seed grows one colony; a noise field nucleates a pattern everywhere at once

Each image below records its exact parameter set.

SELECTED STILLS — 6

COLOUR / FORM = REAL PHYSICS

The visible pattern is the autocatalyst concentration v; colour is mapped to v, and the glow is mapped to the reaction rate u·v² — the amount of catalyst being created right now.

Because reaction only happens where fresh substrate meets the autocatalyst, only the advancing front lights up. Once a stripe has settled and its substrate is spent, it goes matte. The result reads as living tissue: a warm, luminous growing edge over a cool, quiet body.

The palette — tissue, deep navy body ⇄ amber front — is a house colourway. Gray-Scott is an abstract reactor, not a specific chemistry, so its colour is an interpretation of the fields v and u·v², not a measurement.

thin bright network — active fronts F 0.062 · k 0.061

Colour = v · glow = reaction rate u·v² — model quantities, not measurements.

REFERENCES

P. Gray & S. K. Scott, "Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A + 2B → 3B; B → C," Chemical Engineering Science, vol.39, 1087-1097 (1984).
J. E. Pearson, "Complex Patterns in a Simple System," Science, vol.261, 189-192 (1993).
A. M. Turing, "The Chemical Basis of Morphogenesis," Philosophical Transactions of the Royal Society of London B, vol.237, 37-72 (1952).

INTERACTIVE STUDY

A small window into the model behind this study — a deliberately simplified instrument, reduced in resolution, scope, and rendering. The finished works above are something else entirely: parameters swept, frames chosen, and graded by hand from the full engine. Bend the feed and kill rates and watch the morphology switch.

SIMPLIFIED INSTRUMENTGRAY-SCOTT — 2 VAR · LIVELENS — u·v² · REACTION RATE

This interactive study is not intended as a scientifically validated reproduction. It is a visual interpretation generated from an implemented model and curated parameter exploration — and it is a deliberately simplified instrument, separate from the full engine used to author the finished works.