While I was studying geology we had a series of classes on the subject of chaos theory. Our professor was very enthusiastic about fractals and their practical application within geology and other fields. At the time, research was being done using fractals to look for potential economic mineral localities, attempting to predict the seemingly random. To us, it was mostly about the pretty patterns, but his energy and love for the topic was infectious. Can't say I spent a great deal of time afterwards looking further into the theory, but at the time I found it fascinating.
Benoit Mandelbrot, probably the man most associated with chaos theory, died in Massachusetts the other day, aged 85. In the late '70s and early '80s he published breakthrough work which looked at breaking down apparently chaotic natural forms into sets of scaled repeating patterns which built to larger, self-similar forms. The maths of fractals is a little scary, but the patterns are nice... An early form used triangles with three Koch Curves to produce what's called the Koch Snowflake, there's the brilliantly-named Menger Sponge and almost certainly the best-known, the Mandelbrot Set. I recommend spending a few minutes looking through the gallery links from the Wikipedia entry for fractals. Beauty in mathematics. Fractals have since been used to develop techniques of measuring things previously considered unmeasurable - coastlines, mountain ranges, clouds and so on. The parent science of chaos theory will have a huge range of influence - there is a great deal of fruit still to be picked from these strange trees.
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