4(d) For each side length r, we have Nr(B) = 2Nr(A). |
Then Log(Nr(B)) = Log(2Nr(A)) = Log(2) + Log(Nr(A)). |
That is, each point in the log-log plot for B is the corresponding point in the log-log plot for A, but shifted up by Log(2). |
So if the points on the log-log plot for A lie on a straight line, the points on the log-log plot of B lie on a parallel straight line. |
Because the dimension is the slope of these lines, and parallel lines have the same slopes, A and B have the same dimension. |
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