How long is a country’s border? That’s the seemingly simple question mathematician Lewis Fry Richardson asked himself more than 75 years ago.

The thing that puzzled him was that the length of the measuring stick mattered. Let’s use Great Britain as an example: Use a 100-mile ruler, and you get one answer for total coastline. But if you reduce that ruler to a mile, it will fit inside bays the larger ruler missed, and the answer will be far larger. An inch-long ruler will give a still-larger result.

Indeed, Richardson realized, the answer depended entirely on the length of the measuring stick. The shorter it is, the longer the measurement. Taken to its conclusion, the answer was striking: The coastline of Britain is infinite.

He didn’t know it, but Richardson had just stumbled on a previously unrecognized type of geometric object, one that was destined to revolutionize traditional mathematics. He’d found a fractal.