two chemicals, two numbers, and a gradient — spots, worms, mazes and a desert living next to each other on one plate, because the climate is different from east to west.
try this first just watch. The spotted country, the worm country and the empty country are the same reaction. Then pull one climate all the way up: the geography collapses into a single animal. Drag to plant a seed in a climate that has none. Hold X to see the climate without the animals.
U + 2V → 3V, feed F and kill k. Textbook applets pick one (F, k) and show one animal.
Here F increases east and k increases south, so the plate is a living slice of Pearson's 1993 map
— the interesting object is the front between climates, not any single pattern ·
← more sketchesPhilosophy — the genome is two numbers, the animal is a place. Alan Turing's 1952 paper on morphogenesis asked how an embryo gives itself spots without a drawing of the spots. Two chemicals that activate and inhibit each other, diffusing at different speeds, are enough: the same reaction that is uniform in a beaker becomes a skin the moment it has room. Pearson later mapped which two numbers (feed, kill) produce which skin — spots, worms, mazes, a boiling chaos, or nothing. This plate is that map made flesh. Nothing about the chemicals changes from left to right except the climate they live in, and the plate still divides into countries. A spotted nation shares a border with a worm nation, and the border is itself alive: patterns try to invade, fail, or hybridise, depending on which way the numbers tilt. Pull one climate and you are asking the whole world to be one animal. It will try. Watch which country wins.
Technique — Gray–Scott on a climate gradient. The local rule is
Pearson's:
∂U/∂t = Du∇²U − UV² + F(1−U),
∂V/∂t = Dv∇²V + UV² − (F+k)V,
with Du=0.16, Dv=0.08, a five-point Laplacian, and Neumann shores so the
geography has edges rather than wrapping into a torus. What is not textbook is that F and k
are fields. Default window is F ∈ [0.018, 0.038], k ∈ [0.052, 0.063] — a rectangle
chosen by looking, not by formula, because it is the slice where four morphologies and a
desert all fit on one 192² plate. The gradient has to be slow next to a pattern wavelength
or you get soup; 192 cells is just enough for a few spots per climate.
One climate interpolates every cell toward the midpoint (F, k), which is how you
watch an atlas collapse into a specimen. Nuclei are scattered at seed so every climate that
can live, does; drag plants more. Holding X shows the (F, k) field at full ink —
the climate map as a momentary overlay, not a second live encoding.
?lat= slides the window along Pearson's corridor (span unchanged) if you want a
different slice; it is not a visible control.
Aesthetics — hue is climate, ink is life. A Gray–Scott demo usually paints V in one ramp, so a spotted world and a worm world look like the same substance in different arrangements. Here hue is taken from the cell's own (F, k): sage in the spotted west, gold through the worm belt, coral in the maze east. Brightness is V. The empty corner is not a failed render: it is the homogeneous state, the fifth biome, the climate where this reaction cannot make an animal. Switch to ink and the same geography becomes a lithograph: one walnut on cream, climate told only by shape. The pixel scale is honest — nearest-neighbour upscale, no blur. You are looking at the grid the chemicals live on.