An obvious test of this approach is to compute the box-counting dimension for a fractal having known dimension, established by other methods.
Attempts using even relatively simple shapes, such as the Koch curve, were disappointing. Class projects (admittedly with only a few sizes of grid squares) yielded dimension values ranging from 1.1 to 1.4., while the correct answer is about 1.26.
A source of this problem is that the number of boxes
counted at a specific scale is sensitive to the placement of the grid on the picture.
Of course, grid placement does not affect the limit as
We explore this effect in our grid placement investigations.
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