RunTheSim
What is actually running
Call the substrate U and the catalyst V. V eats U to make more V, which is the autocatalytic part. A feed rate tops U back up everywhere on the plate. A kill rate removes V everywhere. Diffusion smears both, but the catalyst spreads slower than the substrate.
That is the whole model. Four moving parts, one plate, and no instruction anywhere that says stripe.
| Control | What it does | What the plate does |
|---|---|---|
| Feed rate F | Replenishes the substrate everywhere | Patterns grow, spread, fill in |
| Kill rate k | Removes the catalyst everywhere | Patterns thin out, break up, die back |
| Diffusion | Smears both, catalyst slower than substrate | Edges stay sharp instead of blurring flat |
| Brush | Paints fresh catalyst onto the plate | The settled pattern reacts around what you drew |
Why the sliders are the point
The two numbers do not describe the pattern. They pick a place in a parameter space, and the plate works out the rest by itself.
Move the feed rate up by a hair and a field of stable dots starts dividing. Nudge the kill rate and the same dots stretch into stripes, then knot into a labyrinth. You did not switch models. You walked two steps across the map that Pearson published in 1993, and the plate reorganised. That map, and the crescent-shaped region where the interesting behaviour lives, is catalogued on Robert Munafo's Gray-Scott pages.
This is why a static picture of a Turing pattern teaches you almost nothing. The picture is one point. The system is the map.
What to look for in a good one
Most pages that rank for this term show you a finished pattern and call it a simulation.
The pattern is the boring part. The parameter space is the simulation.
Five things separate a sim you can think with from a screenshot with a play button:
- Two live sliders, not a gallery of pre-rendered results
- Presets that drop you into genuinely different regions of the feed and kill map, so you can feel the borders between them
- Something to draw with, so you can disturb a pattern that has already settled and watch it repair itself
- Honest notes on what the model leaves out: fixed diffusion ratio, two dimensions, edges that wrap around instead of being walls
- Speed. If a change takes a minute to show, you stop experimenting
The last one matters more than it sounds. Understanding here comes from a loop: predict, change one thing, be wrong, change it back. A slow sim breaks the loop.
Where this shows up outside the browser
The same class of maths goes back to Alan Turing's 1952 paper on the chemical basis of morphogenesis, which argued that stripes and spots can arise on their own from a uniform starting state, with no plan and no designer. The mechanism and its history are summarised in the overview of Turing patterns.
Animal coats, seashell pigment, sand ripples and early limb formation all sit in that family. Not the same equation in every case, but the same idea: local rules, repeated, making a global shape. If you want the concept without the chemistry, the pattern formation page covers it.
A fair warning about the sim itself. It is a two-chemical Gray-Scott model, not a literal lab. The diffusion ratio is fixed, the grid is small, and the colours are a brand choice rather than a chemistry view. It is a thinking tool, built as a solo project in St. Gallen, and it is free to play with the rest of the library.
The fastest way to get this is to move one number yourself: open the Gray-Scott sim, click the presets in order, then drag the brush across a pattern that has already settled.