Sunday, November 30, 2003
In 1967 Benot Mandelbrot pointed out that asking "How long is the coast of Great Britian?" is suprisingly deep. The answer, it turns out, hinges on how long (or how flexible) the ruler is that is used to make the measurement. You can use this physical system (as Mandelbrot did) to develop a geometry of systems that somehow fall between conventional notions of dimensionality.
This paper, by Sapoval and others, proposes that the fractal dimensionality of the coastline springs naturally from the interplay of the three processes at work: energy input to the coast by waves and energy dissipating from the coast either by chemical (chemical dissolution of rock) or mechanical means (breaking big rocks into smaller ones).