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Mandelbrot developed a
method that treated fractals as a part of standard Euclidean geometry, with the
dimension of a fractal being an exponent.
Fractals pack an infinity into "a grain of sand". This infinity appears
when one tries to measure them. The resolution lies in regarding them
as falling between dimensions...
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This infinity appears
when one tries to measure them. The resolution lies in regarding them
as falling between dimensions. The dimension of a fractal in general
is not a whole number, not an integer. So a fractal curve, a
one-dimensional object in a plane which has two-dimensions, has a
fractal dimension that lies between 1 and 2...
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