ANSWER:
1.465
STEP-BY-STEP EXPLANATION:
The generator of the Sierpinski carpet consists of 20 line segments and the initiator consists of 4 ine segment. Thus the replacement ratio is 20:4 or 5.
The initiator of the Sierpinski carpet is a line segment that is 3 times as long as the replica line segments in the generator. Thus the scaling ratio is 3:1 or 3.
The similarity dimension D of a stricty-similar fractal is given by:
[tex]D=\frac{\log N}{\log r}[/tex]
Where N is the replacement ratio of the fractal and r is the scaling ratio. Hence, the similarity dimension D of Sierpinski carpet is:
[tex]\begin{gathered} D=\frac{\log 5}{\log 3} \\ D=1.465 \end{gathered}[/tex]
