Published: December 29, 2010
The mathematician Stephen Wolfram made a bold pronouncement last summer: The universe, in all of its infinite complexity, is the result of less than a handful of computational rules. That is, you plant a tiny seed of incredible simplicity, tell it a few basic things about how to grow, and it will generate a chaotic infinity.
The computational universe is what the thinker calls a “new science” but, in fact, is rooted in a very basic yet extremely recent concept: fractals, the discovery of mathematician Benoit Mandelbrot, who passed away Oct. 14 of pancreatic cancer, some six months after receiving an honorary degree from Johns Hopkins University.
Put simply, a fractal is a geometric shape that does not reduce down to a smooth curve or line. It is infinitely rough and infinitely complex. You could take a simple fractal shape the size of your hand and blow it up past the boundaries of the universe without reaching the “bottom” or end. There are more shapes and details past eternity.
It’s not a quirk or a mathematical trick—fractals are everywhere in the universe: mountains, trees, leaves, coastlines, galaxies. The fractal is nature’s chosen building block. And it took human civilization until 1980 to discover it via a curious French mathematician who decided to run some old mathematical series through a modern computer and discovered the revolutionary ramifications of what’s now known as the Mandelbrot set.
“The thumb print of God.” Infinity itself. Really fucking trippy. All apt descriptors of the Mandelbrot set, a series of points on a plane that describe a very particular shape, like a reclining Buddha, or cat, or hodgepodge of stubby minarets. What it looks like is less important than that it looks the same everywhere. Not everywhere in the from-all-angles sense, but everywhere in the sense of near and far—if you magnify one of its edges you will find more of the initial shape and if you look at the edges of that shape, you will find that shape again. Forever. And the equation that describes it is so basic, it’s unbelievable: /z/=/z/^2 +/c/, where /c/ is a complex number and /z/ is some position on a plane. Simplicity yields infinite complexity.
Mandelbrot was born in Warsaw, Poland, in 1924, though most of his youth was spent in Paris after his family was forced to flee during World War II. With two mathematician uncles and a doctor mother, it’s no surprise he eventually graduated with a doctorate in mathematical sciences from the University of Paris. Over the next 30 years, much of them spent within the research arm of IBM, Mandelbrot developed his fractals, applying the concept to fields as varied as biology and information theory—all of it to explain the previously unexplainable or, in other words, applying fractals to discover the “order within chaos.”
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