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

prized piece was a brown polka-dot nautilus that had been varnished. How many hours had I stared at this store-bought addition to the other shells, most of which I’d found on vacation beaches with my family? I had liked it because it was so clean and glossy. In childhood imaginings, staring at that shell, I saw myself going round and round the spirals like a slide, the spiral never ending and the sound of the ocean echoing in the white halls of my seashell amusement ride. I wondered about my favorite shell’s previous life under the sea and the creature that had inhabited it. How deep underwater had it lived? What had it eaten? Where had it been in its travels? How had it died? How could it be so utterly perfect living in the murky depths until some fisherman or a crashing wave tossing it ashore had led it to me?
    One day, I was bingeing on information again, glued to my chair, sitting in front of the computer in my house for the fourth straight hour. I’d been searching for the repetitive geometric forms I was seeing before my eyes when a nautilus shell appeared in the retrieved entries on my screen. I clicked on it immediately. There was something at once familiar about the spiraling natural form. I’d seen it in my childhood prized possession, but I’d also seen it in my morning coffee as I stirred; I’d watched it every day as the water in the sink went down the drain. And one of the new images I saw repeatedly was a spiral out in space. I often wondered about its seemingly infinite reach and how smaller parts of it echoed the larger parts. But I hadn’t connected that outer-space shape to the nautilus, much less to other things I was noticing in nature, until now. As I read on, I learned that these shapes were known as fractals, a word I’d never heard before. Fractals are the fundamental, repetitive geometric building blocks of everything in the known universe, from seashells to the leaves and trees and mountains and even to lightning. The pull of this newfound discovery was strong. It seemed to signal to me that my visions could be something more than the hallucinations of a brain-injury survivor. It felt like the beginning of a way back to sanity.
    It all seemed to relate to something I’d seen during one early-morning grocery-store run. There was a leafy tree with a branch overhanging the roadway. The leaves became virtually see-through in the glow from my headlights. Each leaf seemed to have its own trunk and branches running through it, mirroring the tree as a whole. I stared in wonder, and then I held my own hand up. I was captivated and quickly flicked on the car’s overhead light to be sure. The veins of my hands branched out under my pale skin like those of the leaves. The tiny wrinkles on my hand also seemed to be a repetitive pattern. My fingers seemed an echo of my arm, my arm an echo of the trunk of my own body.
Why have I never noticed this before?
I thought. I now had respect for the smallest things and was filled with a sense of wonder about the world at large, despite my ongoing fear of it. And as quickly as it had come on, my epiphany passed, overtaken by the paranoia that someone would recognize me with the car light on and try to harm me. I flicked the light off and continued driving.
    I learned all I could about the fractal nature of the seashell and began researching the budding branch of mathematics known as fractal geometry. It was a very young discipline, developed in the 1970s by IBM researcher Benoit Mandelbrot and popularized in the 1980s after the publication of his book
The Fractal Geometry of Nature.
Why is fractal geometry so much more amazing than the stuff most of us learned in school? Textbook Euclidean geometry is what’s used to measure or create smooth shapes—think of the clean edges of a high-rise building, the sleek lines of a countertop, or the symmetrical arch of a bridge. But it tends to fall short when one attempts to measure or reproduce the rough shapes found in