Fractal Lives

My plan was to write about fractals. Since I first learned about them I was fascinated by the concept: Symmetry in nature. Objects that appear to be asymmetrical or randomly constructed have a symmetry – what is referred to as self-similarity, a characteristic in which the component parts resemble the structure as a whole. A fern frond, tree bark, snowflakes, ice crystals, coastlines…the list goes on and on. Fractals were first described in the 1980’s by a man named Mandelbrot. The key characteristic of a fractal is the way it is constructed: With most geometric forms, the closer you look the more they resemble a straight line, but in the case of a fractal, the closer you look the more complexity you see. A simple shape is repeated within the fractal, each iteration increases the number but decreases the size so as you examine the shape more closely you see it repeated over and over and over….getting smaller and smaller and smaller…theoretically into infinity. Computer-generated fractals, like the one shown here, are fascinating and beautiful.

What else could I say about fractals? I had some ideas but I decided I’d better do a little research first. I got to wondering if humans might fit the fractal mold – a person may seem uncomplicated at first glance but on closer inspection we are complex creatures. Hmmm…it makes me think about a previous post discussing the inner depth of the human self that is often unrevealed to those around us. I wonder….how fractal are humans? Physically I supposed that if plants could be fractal, so can animals. If I understand what I’ve read, even DNA has fractal characteristics.

The article Noisy Nucleotides (Scientific American Sept 92 puts it this way: “Commuter traffic, earthquakes and the selection of presidential candidates usually seem to take place in random ways. But investigators of chaos theory who turn to patterns called fractals manage to find order in the midst of such unpredictable events. Now add DNA to the catalogue of things fractal-like.”

In Ecology and the Fractal Mind in the New Architecture: a Conversation Professor Nikos A. Salingaros relates the history of fractals in architecture: “Fractals have two related characteristics: they show complexity at every magnification; and their edges and interfaces are not smooth, but are either perforated or crinkled. A fractal has some connective structure at different scales. Historical cities are richly structured at every magnification, whereas contemporary cities enhance the largest scale but suppress everything else. There are no straight lines in fractals.”

Interesting…..apparently fractals abound everywhere in nature, perhaps even being a key element in the formation of both animate and inanimate natural objects. Many man-made objects as well seem to take on a fractal form. My mind wants to take it one step further: Can our inner selves – our psyches – be said to have a fractal design? In the article referenced above, Professor Victor Padrón says, “It is not difficult to concede that our psyche, which has its assumptions built into the brain, has an essentially fractal structure as well.”

Okay, so after all that research and thought (and reading for those of you who have made it this far) here’s my question: Is this fractal design of nature pure coincidence? Can it be scientifically explained? Is it just another characteristic that can be explained by evolution – change over time? Do fractals support the idea of a supreme hand in the creation of the universe or do they refute it?

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