Two chemicals that activate and inhibit each other can paint the patterns of the natural world.
Two chemicals spread across a surface. U activates growth and produces V; V inhibits U. Both diffuse, but V faster.
U forms peaks where it can outpace V locally; V catches up and pushes it down. The peaks settle into stable spots, stripes, or labyrinths.
This is the Gray-Scott model. Two reactions plus diffusion produces the patterns on leopard fur, zebrafish skin, and seashells.
Figure 1. Gray-Scott reaction-diffusion on a 256×256 grid. Drag the f and k sliders to change the chemistry, speed to change how many integration steps run per frame, and try a different colormap to reveal structure your eye might miss. Click the canvas to drop V seeds by hand; Perturb sprinkles fresh seeds without wiping the pattern.
Feed rate f controls fresh U inflow; kill rate k controls V decay. Together they determine the pattern. A small change can flip the system from spots to stripes or to a pulsing, dividing mass.
The map below shows which (f, k) regions produce which behavior. Dark regions are dead zones; bright regions are where patterns form.
Figure 2. The Gray-Scott parameter landscape. Each pixel is colored by the steady-state behavior at that (f, k) pair. Click to try a region. The named presets mark well-known pattern families.
Initial conditions matter. A single seed grows into spreading coral; a stripe of V breaks into chains of spots; random noise produces the most organic textures.
Draw a circle and it fractures. Draw a line and it beads up into spots.
Figure 3. Paint your own seeds, then watch the chemistry reshape them. The reaction-diffusion process fills, splits, and reorganizes whatever you draw.
Turing proposed the mechanism in 1952, decades before chemicals were observed in tissue. Two substances diffusing at different rates can spontaneously break symmetry. Morphogen gradients have since been confirmed in zebrafish, mice, and many other organisms.