Fractal Dimension
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A fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the Scaling (geometry)|scale at which it is measured. It has also been characterized as a measure of the Space-filling curve|space-filling capacity of a pattern that tells how a fractal scales differently than the space it is embedded in; a fractal dimension does not have to be an integer. The essential idea of fractured Hausdorff dimension|dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions. In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used (#coastline|see Fig. 1). In terms of that notion, the fractal dimension of a coastline quantifies...
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