I read in passing in a newsletter [recently renamed The Marginalian (formerly Brain Pickings)] a mention of “fractals,” a term with which I am familiar but whose definition I have never fully understood. I set aside the newsletter, but the term “fractal” stuck in my head. Later this morning, when I looked up the word, this is the definition I found: “an irregular geometric structure that cannot be described by classical geometry because magnification of the structure reveals repeated patterns of similarly irregular, but progressively smaller, dimensions.”
The definition went on to offer examples: “Fractals are especially apparent in natural forms and phenomena because the geometric properties of the physical world are largely abstract, as with clouds, crystals, tree bark, or the path of lightning.”
A secondary definition, applicable to architecture and decorative art, is offered as follows: “a design or construction that uses the concept and mechanics of fractal geometry.”
Neither definition adequately explained to me the meaning of the word, nor its applicability in the world around me. Only after I searched for images associated with the term did I begin to understand it. Even then, it remained fuzzy until I returned to the natural examples. Finally, while considering the description and another specific graphic example did it begin to become increasingly clear. An abstract tree canopy clarified it for me, as did a magnified image of a snowflake, an enlarged photo of a splash of alcohol ink on a field of pure water, and a photo, taken from space, of a river network. The website of The Fractal Foundation offers what may be a more precise definition; somewhat easier to grasp:
“A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions.”
During the course of growing older, I regularly discover and rediscover the almost incomprehensible beauty of physics. And that discovery upsets me that either I never had the intellectual capacity to understand physics or the ability to regulate my own interests to successfully pursue it or both. I have long since given up on trying to comprehend physics, opting instead to marvel at its incredibly complex beauty and its absolute integration with the natural world around us.
Even now—in what I hope is only the beginning of the very early stages of the long twilight of my life—I still wish I had devoted more of my youth to my own education. I wish I had been smart enough to know how important an understanding of the world and my place in it could have become. If I knew in my youth what I know now, I might have applied myself, even in school subjects that seemed boring at the time. I wish I had been able to appreciate that “practical” knowledge is not the only knowledge worth having. I wish I had understood that the pursuit of “understanding,” in its purest form, is the most valuable gift one can give to oneself. And it is the most meaningful gift one can help others give to themselves.
The beauty of physics and geometry—and fractals—always drives me to appreciate art’s natural attraction. Art captures the mystique and complexity of nature, as if it seizes the importance of never-ending repetition of patterns. Art, whether created with a brush or by hands on a wheel or any other means, uses repetitive patterns of movement to form monuments to the natural world around us. Even abstract art, seemingly unrelated to nature or, indeed, any aspect of the world around us, appropriates observations and translates them into patterns for others to see, if they choose to examine art closely enough.
I cannot adequately explain my thoughts this morning; they are too convoluted to put into clear words. But like so many other days, this morning seems to clearly point me in the direction of “knowing” how important our understanding of the natural world is to our appreciation of life itself. It’s sad to think that most people—like me—fail to devote the time and energy to understanding fractals and physics. If they did, their time on this planet would be more fulfilling, I think. And they would contribute to a more fulfilling time for others. Alas, it’s easy to nourish and hard to starve ignorance, while it’s hard to nourish and easy to starve knowledge.
Grocery stores should open much earlier. Like breakfast restaurants, they should open by 6:00 a.m. at the latest. Only savages stay in bed after 5:30; the rest of us need to be up and productive long before then. And than sometimes means getting breakfast or buying groceries. I admire donut shop/bakery owners and employees; they know the value of “early to rise.” That’s both “pun”-ny and productive.