by Katie Bowell, Curator of Cultural Interpretation
Last Thursday, October 14th, mathematician Benoit Mandelbrot died. Even if you’re not familiar with the name, I bet you’re familiar with images of his work; Mandelbrot was the father of fractal geometry.
According to Mandelbrot, a fractal is
a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole
Before Mandelbrot defined the term “fractal,” the split-able geometric shapes had been noticed by other mathematicians. However, because the shapes defied the rules of Euclidean geometry that governed so much of the world of mathematics, the funny, repeating patterns were classified as oddities; strange “outcasts” of math with unnatural properties. Mandelbrot brought these shapes together and, in the words of a song by Johnathan Coulton about the mathematician, showed that “infinite complexity could be described by simple rules.”
Mandelbrot’s work with fractals and the complexity of roughness is now used to explain, explore, inform and predict patterns in an astonishing number of disciplines: everything from the stock market to vascular surgery.
You may have even looked at some fractals today – they’re found throughout the natural world. Seashells, snowflakes, lightening, ferns, blood vessels, pineapples, mountain ranges, galaxies, shorelines, stalactites, stalagmites and many more natural objects all exhibit the characteristic repeating pattern of fractals. My favorite? Romanesco broccoli.
And fractals aren’t just found in nature. Computer analysis of Jackson Pollock’s paintings has found fractal patterns within what at first may just look like paint splatters and dribbles, and composers are using the theories behind fractals to create new mathematical musical compositions.
Here’s Mandelbrot’s TED Talk, “Fractals and the Art of Roughness.”
And here’s a beautiful visual journey through fractals
Want to learn more about fractals? The best place to start is Mandelbrot’s The Fractal Geometry of Nature.