The Moran Equation

When the SImilarity Dimension Formula Fails

For self-similar fractals made of N copies, each scaled by the same factor r, the similarity dimension d_s is given by

d_s = Log(N)/Log(1/r).

Now consider the fractal shown on the left.

On the right we see it is made of three pieces scaled by r = 1/2 and one piece scaled by r = 1/4.

Because different r values are involved, the similarity dimension formula cannot be applied. What can we do?

Return to the Moran equation.