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Fractal dimension measurement in ImageJ.  Wayne Rasband, NIH. using the Box Counting Method.

To use ImageJ on the solid fractal images here:


Tool source page:

Description from that page:

Calculate the so-called "capacity" fractal dimension.  The algorithm is called, in fractal parlance, the "box counting" method.  In the simplest terms, the routine counts the number of boxes of a given size needed to cover a one pixel wide, binary (black on white) border. The procedure is repeated for boxes that are 2 to 64 pixels wide. The output consists of two columns labeled "size" and "count". A plot is generated with the log of size on the x-axis and the log of count on the y-axis and the data is fitted with a straight line. The slope (S) of the line is the negative of the fractal dimension, i.e. D=-S.

A full description of the technique can be found in T. G. Smith, Jr., G. D. Lange and W. B. Marks, Fractal Methods and Results in Cellular Morphology, which appeared in J. Neurosci. Methods, 69:1123-126, 1996.

This article does not state whether or not the border is 4-connected or 8-connected. Perhaps it makes no difference.