Turing Patterns: The Mathematics Behind Cheetah Spots and Stripes

Where Biology Meets Mathematics

I’m working on a new video about a topic that sits at an unexpected intersection of biology and mathematics. While preparing it, I ran into some fascinating behavior from AI image generators — behavior that turned out to be surprisingly revealing.

The AI Generator Challenge with Animal Patterns

Here’s the thing: cheetahs have spotted bodies and striped tails. I needed to generate the reverse — a striped cheetah with a spotted tail. Neither Midjourney nor DALL-E could pull it off.

Sure, I could have tried Stable Diffusion, or spent more time crafting cleverer prompts. But the point stands: sophisticated AI, for all its capability, can’t simply swap spots and stripes to different locations on demand. It seems that what nature produces effortlessly, AI still finds genuinely difficult. There’s more work to be done — and the result you see in the image above is what I managed to get in the end.

Why Turing Patterns Explain Cheetah Markings

Why spots and stripes at all? And why do cheetahs have that specific pattern — spots on the body, stripes on the tail? That question goes deeper than it looks, and the answer connects directly to Turing patterns: a mathematical model that explains how animal coat markings self-organize during development.

The full explanation is coming in the new video, out very soon.