F: FRACTAL

The 1992 documentary on fractals featuring the iconic scientist Sir Arthur C. Clarke was entitled, “Fractals: The Colors of Infinity.” The title could not be more fitting. Fractals—these marvelously complex shapes generated by surprisingly simple mathematic formulas—give us one of our most literal visualizations of infinity! And guess what? It turns out that (with the addition of just a little computer generated pixilation magic) infinity is blazingly and gloriously colorful! Some even describe the visual effect of fractals as “psychedelic” and the documentary enhances that by using the music of Pink Floyd to accompany “fractal zooms” throughout. With or without music, it is hard not to be wowed by a fractal. The main characteristic of a fractal is “self-similarity”, a trait that manifests as repeating versions of the same shape as one “zooms” through levels of scale. Benoit Mandelbrot, the “father of fractals,” began to inhabit his place in history in the emergent computer world of the 60’s when he realized that a previously unexplainable noise on a channel actually had a pattern that was reproducing itself on several scales. The revolution had begun and a whole branch of math--and life--opened up. We would ultimately learn that FRACTALS were everywhere in nature, not as noise, but as signal! Clouds, ferns, even forest patterns (which it turns out reflect the same branching as the trees they contain) all testify to a universal pervasiveness of mathematical order. Paul Dirac the Nobel Laureate, near the end of a life of religious skepticism, conceded a possible validity to the notion that “God is a mathematician of a very high order and He used advance mathematics in constructing the universe.” Fractals certainly broadcast that reality. In fractals, we see that infinity is not a vast endless void, but rather a coherent superposition of order and beauty—with doses of wild and wonderful chaos dancing between shapes! If the concept of “forever” or “infinite” scares you, reminding you too poignantly of your limited mental ability to control your world, you have not yet seen the colors! Once as a dreamy thoughtful child—with an inner world already far vaster than my outer environment—I struggled with infinity. When I first heard of “eternal” life, I shuddered at the notion of having to manage a forever! Even with my turned-on thinking about all things cosmic, I had met my match in forever-ness. I would later grow to understand the world spiritually and find “forever” as my friend. Infinity still blows my mind, but not in a bad way! I found freedom—instead of performance anxiety—in exploring my connection to Eternity, even in the here and now. Fractals display hope to me, because they say that, no matter the scale—very, very broad and gigantic or infinitesimally small to the point of being invisible—the same truth comes into beautiful apparition on every level! Go ahead and ride a rough and tumble zoom through this mysterious existence—you will only land again and again in rediscovery of the order amidst the chaos! I can’t get past it: LIFE IS GOOD is not just a company slogan—it is the nature of reality. The deep dark areas point to the next iteration of truth decked out in beauty and my confidence grows every time the fractal reappears to my inner eyes after a quest again to see it. It was Benoit Mandelbrot who “discovered” (for he was clear that he did not create fractals, but rather found them there waiting) the world’s most famous fractal, the one that now bears his name. It holds an almost mystical place in pop culture and all one needs do is search YouTube for a “fractal zoom” adding in the word “Mandelbrot” and you will be treated to a whole list of video offerings often set to classical music (as well as a variety of other interpretations). Even if you are not fascinated with the way one very simple formula (Z(n+1) = Zn2 + C) could generate all this beauty, you still may have to admit that there is something incredibly amazing about watching the patterns play out on the screen. Something of your inner need for order seems to connect here and rejoice! I find it fascinating that Mandelbrot, who coined the term “fractal” in the 1975, chose it from the Latin fractus which means broken or fractured, for nothing could make reality appear less broken or fractured than a fractal traced through scale in a dizzying zoom! Maybe this informs our inner world. Maybe, whether he knew it or not, Mandelbrot was sending us a signal: The broken pieces that shout to you of disorder and chaos really are falling into a pattern for good far beyond your current scale! Your limited understanding of this pattern does not preclude its existence! The seemingly broken pieces coalesce kaleidoscope-style into glorious order and beauty when we discover the truth—AND--REMOVE THE “SCALE”! Our notions of scale (time and space that tempt us to shout with clenched fist at the heavens, “Where’s my answer?”) might be to blame for much of our brokenness. The healing prescription might be zooming out and breathing in truth on a universal plane where those culprits of scale temporarily cease to corrupt our view. Some people watch those fractal zooms just because they are “trippy”. I watch them and see a message about the power of the unlimited to inform the now. One more thing: Infinity is not far just far away in the great beyond. It is earthy, right here and now. The correct answer to the question (thank you for this, Dr. Mandelbrot), “How long is the English coastline?” is actually, “It is INFINITE.” Why? Because every little line you make to attempt to draw it could be drawn down with more rough detail, increasing its length….ad infinitum. Infinity is not just in the heavens; it is squarely under our feet…and all around us.