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Dear matson:

Most likely they are statistically self similar, (as opposed to exactly or strictly self similar). When objects are statistically self similar, they need not visually resemble each other, (nor smaller parts of itself). Some examples of statistically self similar objects are clouds or algae blooms or river basins.

They don't look exactly or nearly the same, but they diffuse in an (amazingly) statistically similar way to each other (or to itself at different scales).

For a really good intro to Fractal Analysis get a copy of "Fractals and Chaos, an Illustrated Course", by Paul S. Addison. It explains fractals and chaos in an easy to understand way with some simple exercises.

Benoit Mandelbrot's texts are fascinating but it's like reading Homer's Iliad in Victorian era prose. You'll understand what he's saying after a lot of re-reading and pencil scratching.

Just a personal note: I think that Fractal Analysis is portrayed as the 'holy grail' of analysis. Far from it. However, it seems to me to be an better way to identify similarities in data analysis than the classical Gaussian methods.

Your hyper Fool,
FM
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