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To Figure: To form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern. // The Institute does not yet have a physical space, but our permanent location
in the conceptual landscape is on the edge of this iconic fractal. The Mandelbrot Set belongs to a class of mathematical objects knows as fractals,
whose dimension is always a fractional quantity. Though infinitely complex in form, many fractals are surprisingly easy to generate |
Fractals |
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plan of Ba-Ila village. Image courtesy Ron Eglash |
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| “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” - Benoit Mandelbrot In Ba-Ila villages of Zambia the architectural plan is ordered around a scaling principle that imparts to the whole a fractal structure. Throughout African culture and in Indian paisley patterns, “self-similar” forms containing repeatedly smaller iterations of themselves are a constant motif. Nature too abounds with such structures, drawing upon this concept of recursion in heads of broccoli and cauliflower. Once noticed, fractals are everywhere - in the shape of coastlines and the branching of arteries; in cloud formations and the patterns on seashells; in the structure of fern fronds and the swirling of water over rocks. |
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| Traditional cultures have long known about iterative structures. But not until the late nineteenth century did Western mathematicians begin to explore these forms. To all at the time they seemed monstrous, for they did not fit the classical patterns of Euclid and Newton. Regarded at first as pathological, these aberrant forms were mathematical kin to the cubist paintings and atonal music that were soon upsetting established standards in the arts. In 1975 the great French polymath, Benoit Mandelbrot named them “fractals.” Despite their complexity, many fractals are simple to describe and the rules that generate them are often trivial to state. | ||||
| ©
2005 The Institute for Figuring |
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