The Beautiful Fractals of the Late Benoit Mandelbrot
Benoît Mandelbrot, the French-American mathematician known for his work with fractal geometry, died on Thursday. Mandelbrot lent his name to the Mandelbrot set—the very beautiful, stoner-friendly mathematical object in this video.
Mandelbrot didn't "discover" the Mandelbrot set, but it was named in his honor thanks to his extensive work with it. He also coined the the term "fractal," after spending time thinking about what should be a fairly simple question: How long is the coast of Britain?
The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.
"Here is a question, a staple of grade-school geometry that, if you think about it, is impossible," Dr. Mandelbrot told The New York Times earlier this year in an interview. "The length of the coastline, in a sense, is infinite."
In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a "fractal dimension," an insight that has proved useful well beyond the field of cartography.
The coastline is infinite! How cool is that? Here's another, longer video of the Mandelbrot set, courtesy programmer Michael Hogg Make sure you turn on HD!:
