Box-Counting Dimension

Robert P. Munafo, 1997 Jan 17.

Box-counting dimension is a simple way of estimating the Hausdorff dimension for fractals.

You compute the box-counting dimension from a grid that is superimposed on a fractal image and counting how many boxes in the grid contain part of the fractal. Then you increase the number of boxes in the grid (but covering the same area: the boxes get smaller) and count again. If the number of boxes in the first and second grids are G1 and G2, and the counts are C1 and C2, then you compute a dimension by the formula:

D = log(C2/C1) / log(sqrt(G2/G1))

See delta Hausdorff dimension for a discussion of how the Mandelbrot Set behaves.


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

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