Sunday, November 2, 2008

Nature's Geometry

Benoit Mandelbrot defined fractals in his 1982 book The Fractal Geometry of Nature as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole." Each part resembling the whole, so called self-similarity, allows complexity via layered simplicity. Lots of nature - mountains, clouds, snow flakes, riverbeds, kidneys - are approximate fractals. The notion of a basic four letter code (DNA) utilizing simple geometric replications is very pleasing. The new PBS Nova program on fractals discusses the biological relevance of fractals, including the paradox of biological economy of scale. The biology part is here, entire show can be seen here.

(image credit: Mendelbrot set, Wolfgang Beyer,