| The Universality of Fractals |
| 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. |
| 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. |
| 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. |
Exploring the Infinite
The Universality of Fractals
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