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Reaction–Diffusion

Two chemicals on a grid, one feeding on the other. Spots, mazes and dividing cells out of two numbers, contoured into line work.

Output

A set shares every setting — paper, border, the sketch’s own knobs — and differs only in the seed. Regenerate any one of them without touching the others.

PNG: 3508 × 4961 px at 300 dpi. PDF: vector, RGB, 297 × 420 mm page, no bleed. Printed area 297 × 420 mm.

0 mm

Millimetres of unprinted paper on every side. The piece is composed to fit what is left, not shrunk to fit it.

Chemistry

Named points on the feed/kill plane. Every one is the same equation.

0.0545

Rate A is topped up. Only used when the regime is Custom.

0.0620

Rate B is removed. Only used when the regime is Custom. Most of the plane is dead — the interesting band is narrow.

1.00
0.50

B must be slower than A. Equal rates give nothing at all.

Simulation

150

Cells across. Finer means smaller features and a much slower render.

3000

Most regimes are still moving at 3000 and settled by 6000.

B starts here and nowhere else. The pattern grows outward from it.

12

Drawing

The two are near enough complements of each other, but not exactly.

9
1.00
1.1

Colour

Off draws every contour in one ink, which reads more like an engraving.

How it works

This is the Gray–Scott model. Two imaginary chemicals share a grid. A spreads out and is topped up from outside at the feed rate; B spreads out more slowly and is removed at the kill rate. The only thing coupling them is the reaction A + 2B → 3B, which consumes a unit of A and produces one more B wherever B is already present — so B eats A, and it eats fastest where there is most of it.

That is the entire model, and everything on the page is a consequence of two numbers. Move the feed and kill rates a few thousandths and the same three lines of arithmetic give spots, stripes, a maze, dividing cells or travelling waves. Most of the plane is dead — the pattern either dies out or floods — and the band that does anything is narrow, which is why the regimes are named rather than left to the sliders. B has to diffuse more slowly than A, too: at equal rates nothing happens at all, and that difference in rates is the whole of what Turing proposed in 1952.

The simulation is a raster, but nothing raster is drawn. The finished concentration field is contoured with marching squares at evenly spaced levels, so what lands on the sheet is line work and the print file is a vector. The grid wraps at the edges, which is why the pattern has no border to organise itself against, and it is a fixed grid rather than one the size of the canvas — an A2 is the same picture as the gallery thumbnail rather than a denser relative of it.

R regenerate · S PNG · P PDF