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 ds is given by

ds = 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.