2. B. Box-Counting Dimension

Box-Counting Dimension of the Product of a Cantor Set and a Line Segment

From the observation N(1/3ⁿ) = 3ⁿ*2ⁿ, we can compute the box-counting dimension.

db	= limn->infinityLog(N((1/3)n)) / Log(1/((1/3)n))
	= limn->infinityLog(3n*2n) / Log(3n)
	= limn->infinity(Log(3n) + Log(2n)) / (nLog(3))
	= limn->infinity(nLog(3) + nLog(2)) / (nLog(3))
	= 1 + Log(2)/Log(3)

Note this is the sum of the box-counting dimension of the line segment and the Cantor set.

Return to Box-Counting Dimension of the Product of a Cantor Set and a Line Segment.