Fractals Hunting the hidden dimension

When Benoit Mandelbrot famously asked in 1967, "How long is the coast of Britain?" he pointed out that real coastlines are irregular in a strangely regular way. That is, they look the same at all scales. Thus, you cannot tell if you are looking at a ten-mile stretch of coastline or a one-mile stretch enlarged tenfold. He coined the term fractal to describe geometric objects that exhibit this property of self-similarity. He also pointed out that nature provides numerous examples, such as tree branching, river tributary patterns, and the human circulatory system. With the aid of computers, these curious geometric structures are now playing a significant role in art and science. In a certain sense, they can be said to have fractional dimensions. That is, a sufficiently jagged line is, somehow, more than one-dimensional but not quite two-dimensional like a plane or surface. While the exact definition and proof of this is beyond the scope of a one-hour program aimed at the layperson, nevertheless, this video is fully professional, visually engaging, and well worth watching.-Harold D. Shane, Professor of Mathematics Emeritus, Baruch Coll., CUNY (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.