Seeing Fractals

by Jason Padgett and Maureen Seaberg

Introduction

No one else sees the world the way Jason Padgett does. Water pours from the faucet in crystalline patterns, numbers call to mind distinct geometric shapes, and intricate fractal patterns emerge from the leaves and branches of trees, revealing the intrinsic mathematical designs hidden in the objects around us.

Amazingly, Jason wasn’t born this way. Twelve years ago, he was a party-loving jock and a college dropout who’d never made it past pre-algebra. But a violent mugging permanently and profoundly altered the way his brain works, giving him unique gifts. His ability to understand math and physics skyrocketed. He’s now a devoted student and award-winning artist, hand-drawing the stunning geometric patterns he sees everywhere.

The first documented case of acquired savant syndrome with mathematical synesthesia, Jason is a medical marvel. Some researchers see his transformation as proof that every brain possesses stunning abilities only some people are able to consciously access.

Jason 2.0

If you could see the world through my eyes, you would know how perfect it is, how much order runs through it, and how much structure is hidden in its tiniest parts. We’re so often victims of things – I see the violence too, the disease, the poverty stretching far and wide – but the universe itself and everything we touch and all that we are is made of the most beautiful geometric patterns imaginable. I know because they’re right in front of me. Because of a traumatic brain injury, the result of a brutal physical attack, I’ve been able to see these patterns for over a decade. This change in my perception was really a change in my brain function, the result of the injury and the extraordinary and mostly positive way my brain healed. All of a sudden, the patterns were just…there, and I realize now that my injury was a rare gift. I’m lucky to have survived, but for me, the real miracle – what really saved me – was being introduced to and almost overwhelmed by the mathematical grace of the universe.

There’s a park in my town of Tacoma, Washington, that I like to walk through in the mornings before work. I see the trees that line its path as anyone would, the branches and the bark, but I see a geometrical blueprint laid on top of them too. I see triangular patterns emerging from the leaves, reminding me of the Pythagorean theorem, as if it’s unfolding in the air, proving to me over and over again what the ancient Greek philosopher and mathematician Pythagoras deduced thousands of years ago: the sum of the squares of the legs of a right triangle (a triangle in which one angle is a right angle, or 90 degrees) equals the square of its hypotenuse. I don’t need a calculator to know that the simple formula most of us learned in school – a² + b² = c² – is true; I can see it instantly in the trees all around me. To me, a tree is more than its geometry, but geometry is also far more then most people realize. I think it’s everything.

I remember reading that Galileo Galilei, the Italian astronomer, mathematician, and physicist (and one of my heroes), said that we cannot understand the universe until we have learned its language. He said, “It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it.”

That rings true for me. I see this hidden language of the world before my eyes.

The first thing I do every morning is make my way to the bathroom, turn on the faucet, and let the sink fill up. I watch the water flow and wonder why it doesn’t sound like the strumming of tightly wound strings. The structure of flowing water vibrates in a specific geometric form and frequency to me, and if it were to freeze mid-stream, I’d see a web, but one made up of tiny crystals rather than spider’s silk. If I could hear it after it froze, it would sound like tinkling glass shards falling into the basin. I like to start my days with water. It may slip through my fingers, but it is a constant comfort.

The Infinite can be said to be energy—energy manifesting itself in an infinite number of dimensions and in an infinite number of ways. To look at the world about us, we must first subtract from our consciousness the idea of solidity or mass, we must first understand that there is no such thing as a solid. We are only conceiving such things as solidity in a comparative way, or in a comparative value, with one thing measured against another, as it resides in this terrestrial rate of vibration. We must fully and completely assimilate this constructive philosophy and thus see about us in our world and in our transition of life that the Infinite is manifesting and remanifesting Itself in everything about us. The walls of our home resolve themselves into tiny planetary systems, revolving particles of energy, like the planets around the sun. Their gyrations are, in themselves, functioning according to a certain immutable relationship with the Infinite, for this energy is the substance of the Infinite.” ~ Ernest L. Norman

I look at myself in the mirror and make sure my hair’s not getting too long. I like it cropped close now. I grab my toothbrush and count how many times I run it through the water while brushing my teeth. It has to be exactly sixteen times. I don’t know why I chose that number, but it’s fixed in my mind like my street address or my zip code. I try not to worry about it too much and stare back at the intriguing water webs, working to memorize all the angles so that I can draw a picture of the image later. I’ll probably spend hours with a pencil and ruler later on, capturing on paper every inch of the razor-sharp symmetry.

Next, I walk into the living room and throw back the drapes. If it’s a clear day, I’m in for a real show. The sun comes shining through the leaves of the trees like a million little lights, as if the leaves are blades and they cut the sun up into a million diamonds. Then the rays fan out between the leaves, falling over them like an illuminated net. Watching this, I always think of the famous double-slit experiment, in which light behaves like a particle and a wave at the same time. My friends tell me that to them, it’s just the sun shining through the trees. I can barely remember a time when I saw the world the way most everyone else does.

Next I move on to the kitchen and put on some coffee. It’s one of my routines, but it thrills me every single time I watch the cream being stirred into the brew. The perfect spiral is an important shape to me. It’s a fractal – a repetitive geometric form found everywhere in nature, from the shell of a nautilus up to the Milky Way galaxy. Suddenly it’s not just my morning cup of joe – awesome as the coffee in the Pacific Northwest is – it’s geometry speaking to me again. And I never get tired of it.

All these visions – and every shape I encounter out in the world – correlate with fractals, the elemental geometric building blocks found in nature. Snowflakes, lightning bolts, and coastlines are all fractals, meaning their subsections repeat the same patterns as their wholes. Coastlines are particularly intriguing to me because their overall measurements actually change depending on the scale one uses. For me, this underscores how understanding fractals can shed light on comprehending the nature of other things. For example, I have always wanted to know where humans come from. Now, with one quick glance at human anatomy, I see clearly that veins, arteries, and even the strands of DNA are fractals too. The human body seems to reflect the very structure of creation. The structures within the body reflect the never-ending repeating patterns found throughout the universe. The first time I noticed this, it struck me: everything and everyone is a reflection of this repeating structure.

In the past and especially during the last fifty years, the thinkers and the savants of science have labored and struggled for long periods of time to try to orient or compromise their thoughts into finding the answer to mass and energy. It was only during the last few years of Einstein’s life that this foremost scientist came to the general conclusion that there was no such thing as mass and that we could, in a more abstract way, resolve all things into pure energy. When we have assimilated this concept thoroughly and completely in our minds, we shall have the key to the solution of life, to all principles of life, its creation, its purpose as well as the generic principles which are sustained from the Immortal Mind of the Infinite. In the understanding of the transposition of energy as it manifests itself in numerous dimensions and in different cyclical paths and forms, we shall gain some concept of what the Infinite really is and thus we shall attain some unity with, and see our relationship to it.” ~ Ernest L. Norman

It’s especially important for me to keep drawing my geometry, because that’s how I’m able to share exactly what’s going on in my mind, and I think I’d go crazy if I didn’t have a way to express what I see. By turning my view of the world into drawings, I’ve found a way to explain my universe to others.

I’ve spent plenty of time pondering the very fabric of the universe and how we fit into it. And I’ve concluded that no matter what you go through in life, in the end, there is a symmetry to it all – an order amid the seeming disorder. And if you could see what I see, you’d know that you’re an essential part of that order.

If I could draw the world as I see it and show every last person how he or she is enmeshed in this fine and intricate and impossibly beautiful structure, perhaps people would stop getting lost in the hurt of things and be elevated by the wonder of it all. In fact, I know they would. I know, because even though I seem like the most optimistic man this side of the Rocky Mountains, I’ve been to hell and back.

Excerpt from Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel