Reaction-Diffusion Patterns Screensaver
The Reaction-Diffusion Patterns screensaver runs a real Turing-pattern simulation live, the same simple mathematical model believed to explain animal coat markings. It is free, runs in your browser, and ESC exits.
Live preview
Press ESC to leave fullscreen. Settings are saved in your browser only.
How the Reaction-Diffusion Patterns screensaver works
The saver simulates two virtual chemicals diffusing and reacting across a grid, using the real Gray-Scott reaction-diffusion equations.
Small random seed variations grow into spots, stripes and coral-like patterns as the simulation evolves.
The simulation runs continuously, so patterns keep shifting and never fully settle.
This is the same real class of math proposed by Alan Turing to explain natural patterning.
Turing, Gray and Scott: how simple chemistry makes patterns
In 1952 the mathematician Alan Turing published “The Chemical Basis of Morphogenesis”, a paper on how living things develop shape. His key result was that two interacting, diffusing substances can turn a nearly uniform mixture into a regular pattern: one substance promotes itself and the other, the second inhibits the first, and if the inhibitor diffuses more readily the differences sharpen into waves.
The Gray-Scott model takes its name from Peter Gray and Stephen Scott, who studied the autocatalytic reaction A + 2B → 3B in stirred reactors in a series of 1980s papers. In the pattern-forming version a chemical U is fed in at a steady rate, a second chemical V converts U into more V, and V is removed at another rate. In 1993 John E. Pearson showed in Science that varying the feed and kill parameters produces many different patterns, and mapping that parameter plane has been a popular exercise since.
A caution is warranted when linking this to nature. Reaction-diffusion processes are a basis for morphogenesis and may be related to animal coats and skin pigmentation, and Turing-type models have been applied to fish skin and limb development, but such applications are often models and possibilities rather than settled findings.
A worked example
A single seeded disturbance spreads outward, splitting into a field of spot-like patterns reminiscent of natural animal markings.
Settings & tips
- Accent recolours the pattern gradient.
- Based on the real Gray-Scott model of reaction-diffusion chemistry.
- Patterns never fully settle — the simulation keeps evolving.
Frequently asked questions
- Is this based on real math?
- Yes — the real Gray-Scott reaction-diffusion equations, a well-studied model in mathematical biology.
- Is a key needed?
- No — it is a pure local simulation.
- Is it free?
- Yes — free, no download, in your browser.
- Does the pattern ever repeat?
- No — tiny differences compound over time, so it never repeats exactly.
- What do the feed and kill rates control?
- The feed rate sets how fast chemical U is replenished and the kill rate sets how fast V is removed. Changing them moves the system between different kinds of pattern, which is what Pearson’s 1993 parameter study explored.
- Why do the patterns look organic?
- Because Turing’s ingredients, local activation and an inhibitor that spreads faster, are the kind of mechanism proposed for natural patterning. The shapes are produced by the rules, not drawn by anyone.
- Is the simulation exact chemistry?
- No. It is a simplified mathematical model of two idealised chemicals on a grid, useful because its behaviour is rich and well studied, not because it describes one particular real reaction.