Covering the Koch curve with smaller and
smaller boxes we see the pattern illustrated in the table on the right. 

.
N(1/3) = 3 
N(1/9) = N((1/3)^{2}) = 12 = 3⋅4 
N(1/27) = N((1/3)^{3}) = 48 = 3⋅4^{2} 
and in general 
N((1/3)^{n}) = 3⋅4^{n1}  
Here is the LogLog plot to estimate the
boxcounting dimension of the Koch curve. 
In this case, the pattern is simple enough that we can find the
exact value of the dimension. 
