Box-Counting Dimension of the Koch curve

From the relation N((1/3)n) = 3⋅4n-1 we can compute the exact value of db for the gasket.

db = limrn→0Log(N(rn)) / Log(1/rn) = limn→∞Log(N(rn)) / Log(1/rn) = limn→:∞Log(N((1/3)n)) / Log(1/((1/3)n)) = limn→∞Log(3⋅4n-1) / Log(3n) = limn→∞((n-1)⋅Log(4) + Log(3)) / (n⋅Log(3)) = limn→∞(n⋅Log(4) - Log(4) + Log(3)) / (n⋅Log(3)) = limn→∞(n⋅Log(4))/(n⋅Log(3)) + (-Log(4) + Log(3))/(n⋅Log(3)) = Log(4)/Log(3) ≈ 1.26186

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