Ive got a question regarding the Sierpinski Carpet. I don't understand the intuition behind the formula N = r ^ D where N is the number of squares, r is the scale factor and D is the dimension. In other words I don't understand how by knowing N, r and D you can draw a Sierpinski Carpet.

The other thing I don't understand is why you would take logs of both sides to find D? why cant you just find it using D = logr(N)?

Mr F says: You can. But that's not gonna be too handy unless your calculator has a button, is it?
Is it because the only way that that would work is if we have logD(r^D)? In which case why is that impossible to do?