fractal dimension

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A generalization of the usual idea of dimension that permits non-integer values. For a plane set of points, the fractal dimension is estimated as follows. A lattice of square boxes of side s is superimposed over the set. The number, N(s), of these boxes that contain a portion of the set is determined. This is repeated for a range of values of s. When ln{N(s)} is plotted against −ln(s) the result will be an approximate straight line. The fractal dimension is the slope of this line. An ordinary curve has a fractal dimension equal to 1. Any set of points in a plane has a fractal dimension not greater than 2.

Subjects: Probability and Statistics.

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