Fourth Homework Set Answers

11. Using the product rule for dimensions

dim(C × C × C) = dim(C) + dim(C) + dim(C)

Then the condition dim(C × C × C) = 1 gives dim(C) = 1/3.

The similarity dimension formula gives Log(N)/Log(1/r) = 1/3. Set N = 2 and solve for r, obtaining r = 1/8.

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