40. Referring to Figures 4.41 and 4.42, the Cantor set structure is
apparent. The length of the two intervals remaining in Figure 4.41 is determined by
the intersection of y = s*x and y = 1, and by the intersection of y = s*(1  x)
and y = 1. Both intervals have length s. That is, the Cantor set is covered by two
intervals of length s. A similar calculation shows at the next step we have four intervals
of length s^{2}. So we have N(s) = 2, N(s^{2}) = 4 =
2^{2}, and in general, N(s^{n}) = 2^{n}. The boxcounting
dimension is the limit as n becomes large of the ratio log(2^{n})/log(s^{n})
= log(2)/log(s).
