Table 1.

Data for the four self-similar fractals studied here. As discussed in Section 3.2, lower values of α appear to yield better dimension estimates when ${\text{comp}}_{P{H}_i}\left(X\right)\ne 0$.

Example	True Dim.	${\text{comp}}_{P{H}_0}\left(X\right)$	${\text{comp}}_{P{H}_1}\left(X\right)$	${\text{comp}}_{P{H}_2}\left(X\right)$
S	$\frac{\text{log}(3)}{\text{log}(2)}$	0	$\frac{\text{log}(3)}{\text{log}(2)}$	−
C × I	$1+\frac{\text{log}(2)}{\text{log}(3)}$	$\frac{\text{log}(2)}{\text{log}(3)}$	0	−
C × C	$\frac{2\text{log}(2)}{\text{log}(3)}$	$\frac{2\text{log}(2)}{\text{log}(3)}$	$\frac{2\text{log}(2)}{\text{log}(3)}$	−
M	$\frac{\text{log }(20)}{\text{log}(3)}$	0	$\frac{\text{log }(20)}{\text{log}(3)}$	$\frac{\text{log }(20)}{\text{log}(3)}$