In 1952 Alan Turing asked a question that sounds almost naive: if an embryo starts as a nearly featureless ball of cells, where do its stripes and spots come from? His answer was that you need only two diffusing substances — one that activates, one that inhibits — moving at different speeds. From a near-uniform start, tiny fluctuations get amplified into a stable, repeating pattern.
The model above is the Gray-Scott version: two chemicals, a feed rate, and a kill rate. That's the entire specification. Nowhere is the pattern itself described — no spot is placed, no stripe drawn. Slide the regime and the same equations produce mitosis-like division, coral, mazes, or crawling worms. Click to inject more and watch the system heal back into pattern. (It's a live simulation — give it a moment to develop.)
It is the deepest version of the theme running through this whole guide: structure is not the same as a plan. The leopard's coat, the flock's turn, the company's order — none of them are stored anywhere as a picture. They are what a set of simple, local interactions reliably produces.
Source: Turing, “The Chemical Basis of Morphogenesis” (1952) ↗