Box-Counting Dimension
Practice Problem 1 Answer
From the relation
N(1/3
n
) = 5
n
, we compute the box-counting dimension
d
b
= lim
n→∞
Log(N(1/3
n
))/Log(1/(1/3
n
))
= lim
n→∞
Log(5
n
)/Log(3
n
)
= lim
n→∞
(n⋅Log(5))/(n⋅Log(3))
= Log(5)/Log(3) ≈ 1.46497.
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Practice Problem 1 Answer
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