To accomplish this method, a series of different box sizes d are laid over the
object and the program works by tallying the number of boxes filled during each box size
overlay. One of the problems with this method is that the boxes are weighted the same
whether the entire box is full or just a tiny portion. The information dimension method
addresses this problem by assigning weights to the boxes so boxes containing more
points are counted more than the boxes with fewer points (Benoit 1.3). Unfortunately
this makes the mathematics involved much more complicated.
Ruler Dimension
Mandelbrot (1977) examined the coastline of Britain and determined that this
object was fractal. How was the fractal dimension of this jagged, self-similar line
calculated? The method he used is now referred to as the ruler, or yardstick, method.
The ruler method Dr is defined as:
N(d) & d Dr
where N(d) represents the number of steps taken to walk a divider (or ruler) that is length
d. According to Benoit 1.3, the formal equivalence between this method and the box
dimension can be shown mathematically. Algebraically, this claim is logical, since the
box dimension is simply the reciprocal of the ruler dimension.