A fractal is like an infinite version of a Russian nesting doll.
Unexpectedly, the length of a country’s coastline depends on your ruler. As the measuring stick gets shorter , it can better fit within Great Britain’s nooks and crannies. The shorter the ruler, the longer the coastline. Alison Mackey/DiscoverHow long is a country’s border? That’s the seemingly simple question mathematician Lewis Fry Richardson asked himself more than 75 years ago.
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.Snowflakes form fractals in real life, not just in Koch’s mathematical imagination. Ice crystallizes around a speck of dust in the atmosphere, and the shape of the water molecules results in six-sided symmetry.
What you get has a similar quality to a real-life coastline — and the more steps you complete in constructing it, the longer the perimeter gets. Do it forever, and you’ll end up with an infinitely long border — though all that infinitude still contains a finite area. It’s like a mathematical version of a saying by the 13th-century poet Rumi: “You are the entire ocean in a drop.”In 1978, mathematicians Robert W.
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