Turing Pattern Generator
Grow a Turing pattern and print it: two virtual chemicals, u and v, spread across a grid and react, and from a few seeded squares they settle into spots, stripes, mazes or holes. This tool solves the Gray–Scott reaction–diffusion equations step by step in your browser on a grid of 32 to 256 cells each way whose edges wrap round, so the result is a tile that repeats with no seam. Set the feed rate F and the kill rate k, the grid, the steps (up to 20,000), the seed and the number of seed squares, then draw where v is above a threshold as two-tone cells, as shades, or as smooth contour lines. The tool counts the dark and light patches and says whether the result is spots, holes or stripes and mazes. Repeat the tile up to 4 × 4 and download a PDF, a 300 DPI PNG or an SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). Real size prints on one sheet when the drawing fits; the check bar in the footer lets you confirm the scale. The SVG holds the drawing at the printed size.
Pattern
Look
Page
Runs in your browser with our own code: nothing you type is uploaded or saved. Every step of the Gray–Scott equations is worked out by our own code on the grid shown. You may use what you make here, including commercially, with no credit needed.
How to grow and print a Turing pattern
- Pick a preset, or set F and k.
- Set the grid size, the steps, the seed and the number of seed squares, and wait for the preview.
- Choose two-tone cells, shades or contour lines, the threshold and the colour.
- Repeat the tile if you like, choose Fitted to one page or Real size and the paper.
- Download the PDF and print at 100% (Actual size), or the PNG or SVG.
What you can use it for
- Seamless pattern tiles for fabric, wrapping paper and backgrounds
- Maths, chemistry and biology lessons on reaction–diffusion models
- Posters and wall art of spots and mazes
- Plotter, laser and vinyl art from the contour SVG
- Textures for games and 3-D work
- Comparing F and k values side by side
The 15 presets
| Preset | F | k | Grid | Steps | Seed squares | Dark | Dark / light patches | Shows | Look |
|---|---|---|---|---|---|---|---|---|---|
| Spots: F 0.0367, k 0.0649 (the values Karl Sims calls mitosis) | 0.0367 | 0.0649 | 128 × 128 | 8,000 | 30 | 21% | 75 / 1 | spots | two-tone cells |
| Stripes and mazes: F 0.029, k 0.057 | 0.029 | 0.057 | 128 × 128 | 8,000 | 30 | 42.4% | 1 / 5 | stripes and mazes | two-tone cells |
| Stripes and mazes: F 0.0545, k 0.062 (the values Karl Sims calls coral growth) | 0.0545 | 0.062 | 128 × 128 | 8,000 | 30 | 53.4% | 2 / 20 | stripes and mazes | two-tone cells |
| Holes: F 0.039, k 0.058 | 0.039 | 0.058 | 128 × 128 | 8,000 | 30 | 71.2% | 1 / 74 | holes | two-tone cells |
| Spots: F 0.03, k 0.062 | 0.03 | 0.062 | 128 × 128 | 8,000 | 30 | 23.2% | 89 / 1 | spots | two-tone cells |
| Spots: F 0.025, k 0.06 | 0.025 | 0.06 | 128 × 128 | 8,000 | 30 | 25.8% | 71 / 1 | spots | two-tone cells |
| Spots, far apart: F 0.014, k 0.054 | 0.014 | 0.054 | 128 × 128 | 8,000 | 60 | 8.3% | 34 / 1 | spots | two-tone cells |
| Stripes and mazes: F 0.062, k 0.061 | 0.062 | 0.061 | 128 × 128 | 8,000 | 30 | 66% | 1 / 27 | stripes and mazes | two-tone cells |
| Holes: F 0.046, k 0.0594 | 0.046 | 0.0594 | 128 × 128 | 8,000 | 30 | 89.5% | 1 / 39 | holes | two-tone cells |
| Stripes and mazes: F 0.022, k 0.051 | 0.022 | 0.051 | 128 × 128 | 8,000 | 30 | 45.4% | 1 / 19 | stripes and mazes | two-tone cells |
| Stripes and mazes as contour lines: F 0.029, k 0.057, line at v = 0.2 | 0.029 | 0.057 | 128 × 128 | 8,000 | 30 | 42.4% | 1 / 5 | stripes and mazes | contour lines |
| Stripes and mazes in three shades: F 0.0545, k 0.062 | 0.0545 | 0.062 | 128 × 128 | 8,000 | 30 | 53.4% | 2 / 20 | stripes and mazes | shades |
| Spots as a seamless tile repeated 2 × 2: F 0.0367, k 0.0649, 96 × 96 | 0.0367 | 0.0649 | 96 × 96 (× 2 × 2) | 8,000 | 30 | 20.8% | 43 / 1 | spots | two-tone cells |
| Stripes and mazes, large field 256 × 256: F 0.029, k 0.057, 4,000 steps, 120 seeds | 0.029 | 0.057 | 256 × 256 | 4,000 | 120 | 42.4% | 2 / 13 | stripes and mazes | two-tone cells |
| Holes at real size: 64 × 64 at 2.5 mm, F 0.039, k 0.058, 6,000 steps | 0.039 | 0.058 | 64 × 64 | 6,000 | 8 | 71.3% | 1 / 20 | holes | two-tone cells |
Every count is worked out by the tool from the field it draws (dark = v at or above 0.2).
How the result is named
| Name | Rule (computed on the tile, edges wrapping round) |
|---|---|
| Spots | 8 or more separate dark patches, none bigger than 5% of the tile |
| Holes | One dark region with 8 or more separate light holes, none bigger than 5% of the tile |
| Stripes and mazes | Everything else with both dark and light parts |
| No pattern (uniform) | No dark cells at all, or almost all dark |
Checks
| Check | Result in our tests |
|---|---|
| Uniform u = 1, v = 0 | stays exactly the same |
| Laplacian of a constant field | 0 everywhere, edges included |
| Same start copied 2 × 2 on a grid twice the size | the result copied 2 × 2, bit for bit |
| Same seed twice | the same field, bit for bit |
| Range of u and v over all presets (end of run) | from 0.000 to 0.987 |
| Second solver of our own | agrees to 1e−12 |
What prints
| Download | What is in it |
|---|---|
| The tile (or its repeats) fitted to one page or at real size, vector, with the counts, the range of v and a check bar | |
| PNG 300 DPI | The same sheet as a picture |
| SVG | The tile at the printed size: cells as exact rectangles, one path per colour, or the contour as one stroked path |
For a cutter that needs DXF, use SVG to DXF.
Which tool to use
| You want | Use |
|---|---|
| Spots and stripes grown by reaction–diffusion | Turing Pattern Generator (this page) |
| Cells split by nearest points | Voronoi Generator |
| Random noise textures | Noise Texture Generator |
| Repeating geometric SVG tiles | SVG Pattern Generator |
| Contour lines of a height map | Topographic Map Generator |
Other tools: the Voronoi Generator splits a page into cells, the Noise Texture Generator makes noise textures and the Topographic Map Generator draws contour maps.
More free tools
Grids, patterns and printables?
Drawing and print tools that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What is a Turing pattern?
A pattern that forms by itself when substances react and spread at different speeds. Alan Turing proposed this mechanism in 1952 in “The Chemical Basis of Morphogenesis” (Philosophical Transactions of the Royal Society of London B, volume 237); the Wikipedia article on that paper (read 12 November 2026) says such patterns have come to be known as Turing patterns. This tool draws them with one well-known reaction–diffusion model, Gray–Scott.
What equations does it solve?
The Gray–Scott model: the change of u is Du times the Laplacian of u, minus u v², plus F (1 − u); the change of v is Dv times the Laplacian of v, plus u v², minus (F + k) v. Here Du = 0.2 and Dv = 0.1 in grid units, the Laplacian is the sum of the 4 neighbours minus 4 times the cell, and each step adds the change once (time step 1), which is inside the stable range for these values. Our tests check the tool against a second solver of our own written straight from the equations.
What are F and k?
F is the feed rate: how fast u is topped up towards 1. k is the kill rate: how fast v is removed, on top of F. Small changes to either move the result between spots, stripes and holes, and some values give no pattern at all: with F 0.078 and k 0.061 the presets’ start dies away to a uniform field (worked out by the tool).
Who mapped the patterns?
John Pearson’s paper “Complex Patterns in a Simple System” (Science, volume 261, pages 189–192, 1993) showed the variety of patterns the Gray–Scott model makes as F and k change. The values in two presets, F 0.0367, k 0.0649 and F 0.0545, k 0.062, are the ones Karl Sims’s reaction–diffusion tutorial calls mitosis and coral growth (both read 12 November 2026); the preset names here say what the tool’s own result shows.
How does the tool name spots, stripes and holes?
It looks at the cells where v is at or above the threshold. Spots: 8 or more separate dark patches and none bigger than 5% of the tile. Holes: one dark region with 8 or more separate light holes, none bigger than 5%. Stripes and mazes: everything else with both dark and light parts. Every count on this page is worked out by the tool, and our tests check the patch counts with a second count of our own.
Why does it tile with no seam?
The grid’s left edge touches its right edge and its top touches its bottom, so no cell is on an edge. Our tests show it: the same start copied 2 × 2 on a grid twice the size gives the result copied 2 × 2, exactly, and moving the start moves the result by the same amount. The contour lines are traced across the joins too.
What are the looks?
Two-tone fills every cell where v is at or above the threshold (or below it, with Swap dark and light). Shades split v into 2 or 3 bands above the threshold. Contour lines trace the line where v equals the threshold, between the grid points, with straight segments through each square of 4 points.
Does it model animal coats?
No. It solves one set of equations with the values you choose; it makes no claim about how any animal’s markings form.
How big can it go?
Grids up to 256 × 256, up to 20,000 steps, and up to 270 million cell-steps in one run; every preset draws in under 2 seconds in our tests. The values u and v stay between 0 and 1 on every preset in our tests.
Can it print at real size?
Yes, when the drawing fits on one sheet: choose Real size and set the cell size. Every printed cell is within 0.2 mm of its true place and size in our tests, on US Letter and A4, as long as you print at 100% (Actual size); the check bar in the footer lets you confirm the scale. Bigger drawings print fitted to the page.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. Every step of the equations is worked out by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.