One of the great mathematicians of the past 50 years died earlier this week. (NYT) He is best known for his ground-breaking work on "fractals."
"Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently." -Benoit MandelbrotA TED talk by Mandelbrot.
A fractal is "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," a property called self-similarity.
|Fractal known as the Mandelbrot set, named for Benoit Mandelbrot.|
Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.
Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. The connection between fractals and leaves are currently being used to determine how much carbon is contained in trees.
|Frost crystal shows natural "fractal"|
A 3-D video of fractals:
Mandelbox Zoom from hömpörgő on Vimeo.