Academic journal article The Hudson Review

In Praise of Fractals

Academic journal article The Hudson Review

In Praise of Fractals

Article excerpt

Euclid's geometry cannot describe,

nor Apollonius', the shape of mountains,

puddles, clouds, peninsulas, or trees.

Clouds are never spheres,

nor mountains cones, nor Ponderosa pines;

bark is not smooth; and where the land and sea

so variously lie

and lightly kiss, is no hyperbola.

Compared with Euclid's elementary forms,

Nature, loosening her hair, exhibits patterns

(sweetly disarrayed, afloat, uncombed)

not simply of a higher degree n

but rather of an altogether different

level of complexity:

the number of her scales of distances

is almost infinite.

How shall we study the morphology

of the amorphous? Benoit Mandelbrot

solved the conundrum by inventing fractals,

a lineage of shapes

fretted by chance, whose regularities

are all statistical, like Brownian motion,

whose fine configurations

turn out to be the same at every scale.

Some fractal sets are curves

(space-filling curves!) or complex surfaces;

others are wholly disconnected "dusts";

others are just too odd to have a name.

Poincare once observed,

there may be questions that we choose to ask,

but others ask themselves,

sometimes for centuries, while no one listens.

Questions that ask themselves without repose

may come to rest at last in someone's mind.

So Mandelbrot in time

designed his fractal brood to be admired

not merely for its formal elegance

as mathematical structure,

but power to interpret, curl by curl,

nature's coiffure of molecules and mountains. …

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