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Theory.org » intro » The Universality of Fractals
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The Universality of Fractals
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What are fractals? Fractals are repetitions of the same general patterns, even the
same details, at both ascending and descending scales. They tell us that the
universe and all that it contains is made up of folded realities within self-similar
worlds. The term fractal itself was invented by Benoit Mandelbrot, an IBM
researcher, to describe the new geometry of shapes that form in the wake of dynamic
systems.
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Fractal patterns are all around us, above us, within us. Trees are fractals, with
their repeated pattern of large and small branches, with similar details found even
in the smalleset twigs. Even a single leaf shows fractal repetitions of the whole
tree in both its shape and the branching in its veins. Examine a broccoli or a
cauliflower, and you find fractal geometry at its best, with florets arranged in
self-similar scales; for a total fractal experience, peel the leaves from an
artichoke. Photographs taken through electron microscopes and far-ranging telescopes
reveal that images from vastly different scales evoke a feeling of similarity and
recognition. A spiral nebula that measures hundreds of light-years across looks
remarkably similar to something that measures a thousandth of a centimeter, say the
eye of a firefly. One can be seen as the fractal resonance of the other, the
resonance of the microcosm to the macrocosm. The patterns in the weather, the
turbulence in the winds, the rhythm pounded out by an African drummer, the rituals
performed by queens and shamans and celebrants of the New Year, the courtship habits
of peacocks and prairie dogs, the landscapes of nature and the inscapes of dreams
--- all embody fractal phenomena.
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These examples point to the universality of the fractal as a central organizing
principle of our universe; wherever we look the complex systems of nature and time
in nature seem to preserve the look of details at finer and finer scales. Fractals
show a holistic hidden order behind things, a harmony in which everything affects
everything else, and, above all, an endless variety of interwoven patterns.
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- Jean Houston,
A
Mythic Life
Harper Collins Publishers, Inc., 1996, pp. 6-7.
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