Free Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel by Jason Padgett, Maureen Ann Seaberg Page A

nature, such as clouds, craters, or those coastlines I mentioned earlier. Mandelbrot’s fractal geometry finally gave us a way to explore and understand the natural roughness in the world around us.
    Mandelbrot came up with the concept of fractals while at IBM, where, amid all the number crunching and analysis, he began noticing repeating patterns within the data. He applied a simple mathematical formula, which has since become known as the Mandelbrot set, to the patterns he detected. I know that not everybody is as enthralled with fractal geometry and math as I am, but I can’t help but share the actual formula. I think even math-averse people would have to admit that it looks surprisingly simple:
z
n+1
= z
n 2
+ C.
Where it gets tricky is that it involves complex numbers (a complex number is made up of two real numbers and one imaginary number). And to complicate things even more, every time you solve for
z,
you plug that new value back into the equation recursively and build it out, so the results never end. It can go on literally to infinity.
    Things really got exciting when Mandelbrot put the powerful computing technology at IBM to work, letting the computers apply the formula over and over and over again—more times than any human possibly could. Next, he used the new technology to plot out a visual representation of the formula. The result? A breathtaking image of a fractal so intricately detailed that I could look at it on my computer and hit the zoom button ten times—or, if my computer would let me, a thousand, a million, or even a billion times—and see smaller and smaller subsets of similar but not quite identical patterns. Because of the Mandelbrot set’s intricate patterns and never-ending nature, experts have said that the set may be the most complex of all mathematical objects.
    The Mandelbrot set has captured popular imagination, outside of the realm of mathematics, for many reasons. For one thing, when plotted out, it’s a very beautiful image. In a 2010 TED talk, Mandelbrot explained that depending on the specific numbers he plugged into the formula, the computers spit out shapes of “such complication, such harmony, and such beauty.” He was absolutely right. I stared at the paisley- and ice-crystal-like images I found online and was awestruck and inspired. For some people, the Mandelbrot set is a glimpse into the infinite nature of the universe. Others see it as a way to find order in our chaotic world. Still others consider it a representation of the similarity shared by everything and everyone on this planet.
    For me, it was a reflection of what was going on in my own mind—on a smaller scale, of course. Perhaps my mind wasn’t processing what it saw on the same infinite scale Mandelbrot found, but I do think that what I experience is somehow a reflection of his work. Just as the Mandelbrot set reflects the universal order of things in nature (it has been referred to as “God’s thumbprint”), I believe what I’m seeing is the very essence of ourselves and our universe.
    One day I watched a documentary called
The Colours of Infinity.
It featured Mandelbrot and was hosted by the great science and science fiction writer Sir Arthur C. Clarke, who may be best known for cowriting the screenplay for the film
2001: A Space Odyssey.
Of course, I loved learning more about fractals, but what was most astounding to me was an interview with Michael Fielding Barnsley of Great Britain. A mathematician and author, he founded a company called Iterated Systems Incorporated and works on fractal models that can be applied to technology and even medicine. It occurred to me for the first time that while my visions were nice to look at, they might also have useful applications.
    The deeper I looked into the application of fractals, the more I felt that what I was seeing wasn’t so alien after all. Mandelbrot himself said in the documentary that humans might have discovered his set at any point in human