Grow a pattern

Chemical world

Pattern

Branching channels slowly meet and reorganise.

Feed A 0.0545

Remove B 0.0620

Small rate changes can transform the whole pattern. Some combinations naturally fade into a uniform field; choose a pattern and reseed to start again.

Time & touch

Evolution speed 6

Growth mode

Renewing growth gently refreshes a small patch with fresh A and a B seed, leaving the surrounding pattern intact. At speed 6, renewal begins after 20 seconds and repeats every 10 seconds. Fixed chemistry adds no external disturbances and may settle naturally.

Brush radius 10

Enable Interact and draw to add B. Space pauses and R reseeds when the canvas is focused. Painting also works while paused.

Colour, lighting & quality

Colour palette

Exposure 1.15

Glow 0.55

Relief 0.7

Exposure sets brightness, Glow softens bright highlights, and Relief lights the surface detail. These controls change the appearance without changing the simulation. Set Glow to zero for a crisp view.

Chemical grid

Grid changes restart the field. Colour and relief are artistic mappings of B concentration. They do not change the chemistry.

How the patterns form

The Gray–Scott model couples two dimensionless chemical fields, A and B. A feeds the reaction A + 2B → 3B; B is removed, while both substances diffuse. A spreads twice as quickly as B here. Local feedback and spreading can turn a few chemical patches into complex patterns.

∂A/∂t = D_A ∇²A − AB² + f(1 − A)

∂B/∂t = D_B ∇²B + AB² − (f + k)B

This explorer uses a periodic grid: a pattern leaving one edge continues from the opposite edge. Each step uses a nine-point diffusion stencil, D_A = 1, D_B = 0.5 and Δt = 1. Every preset starts with sparse chemical seeds, with no hidden fast-forward: you can watch colonies grow and meet at a consistent playback speed. This is a mathematical pattern model, not a prediction of a particular real chemical experiment.

Fixed chemistry follows the equations above. Renewing growth adds a local external supply: over 120 simulation steps, a soft circular patch is replenished with A around a small B seed. Renewal starts at step 3,600 and repeats every 1,800 steps, creating room for new growth without restarting the whole field. Feed and removal rates stay fixed; changing playback speed changes how quickly both the chemistry and renewal unfold.

Try changing one thing

Start with Coral labyrinth, pause it, and draw across a channel. Resume to see the disturbance heal or branch. Then try Dividing cells and watch the dots elongate. Changing the feed and removal rates explores different regimes; changing the palette only changes how you see them.

Explore the model and its pattern catalogue in the MIT Gray–Scott reaction–diffusion demonstration, based on John Pearson’s study of complex patterns in a simple system.