whatTwo chemicals in a dish and nothing else: U feeds in everywhere, V eats U to make more of itself, both diffuse -- V at half the pace. Pearson's map of what those three sentences can do is one of the wonders of applied mathematics.
whyThe claim: walking two knobs -- feed and kill -- visits whole biologies. Spots like scattered cells; worms; labyrinths that fill the dish with one wandering corridor; and in one corner, MITOSIS: spots that grow fat, pinch at the waist, and divide, again and again, until the dish is full. None of it is drawn; all of it is measured. A live blob census tells the regimes apart -- count, roundness (4 pi A over P squared), coverage -- and in the mitosis corner the census GROWS, births counted as blobs pinch in two. Drag to stir the chemicals and watch the pattern heal in its own idiom.
howThe Gray-Scott equations on a 160 by 120 lattice, five-point Laplacian, the classic Du 0.2 / Dv 0.1; the double-walled contour rendering is marching squares at two thresholds of V. The story walks spots, worms, labyrinth, mitosis, twenty-six seconds each without resetting the field, so each regime digests the last one's corpse. Everything seeded.