I found it in a high school math book, amongst equations and dry mathematical theory. If you blurred your eyes, the pages of that book would blur together into a fuzzy gray mass, each page indistinquishable from the next. This however was a small, but colorful image in the midst of this grayness, strangely out of place in this book. The image had brightly colored swirls and eddys, resembling firs, palm fronds, oil in water. As you looked closer at the image, more interesting shapes, similar, but slightly different, repeated throughout the image. It totally sucked me in.
It was the Mandelbrot Set, a fractal. It was a small mathematical equation, where esentially the result of the equation was fed back into the equation, repeatadly. It utilized intriquing concepts like imaginary numbers and iterations. The result of this, was this amazingly complex and beautiful image, which didn’t look like any of the normal boring graphs that usually result from equations.
Fractals appealed to the artist, creator, and explorer in me. I was intriqued with the ideas of infinity, complexity, and for the first time in working with math, unpredictability.
I have always loved art, and while the beautiful images of the Mandelbrot set and other fractals certainly resembled art, they were natural. It’s a bit like calling a tree, or the Grand Canyon art. But they were undeniably beautiful. I think the real art of working with fractals is a bit like photography, the art is in the composition, color, and patience required to appreciate the natural. A fractal is a landscape, and the artist in me composes and decides colors and how best to represent what nature provides, much like a landscape photographer composes their images of the natural landscape. Like the photographer who waits and waits, and then waits some more for the right lighting, the right composition, or for the animal to come back within view, generating a fractal is an exercise in patience. Get the composition right and let the computer calculate, which can sometimes take days, weeks, and even months.
Because a fractal is infinitely large, there are areas of the Mandelbrot set that human eyes will never see. Even now, in my modest attempts at delving ever-deeper into it, I could be looking at areas that no one else has ever explored. As someone who enjoys exploring the physical world, working through the Mandelbrot Set and other fractals generates a bit of a pioneering spirit. I look at them with the same vigor that I explore maps. With a map, my interest generally lies with wanting to explore a place physically. When scouring a fractal image, I see locations and places that I want to explore in greater detail, and to drill down deeper into the depths.
Fractals seem like what we see in nature and the world around us, and in them a mysterious sense of something deeper that I can’t quite place. It’s something that is leading us to deeper into the nature of reality and the world around us, and that there is more to explore and discover. Perhaps when we fully unravel the universe and all is understood, we’ll look back at these beaufiful images of iterated equations and recognize them as among the first strings being pulled.