Box-Counting Dimension of the Cantor Set

From the realtion N((1/3)ⁿ) = 2ⁿ we see

d_b = lim_n->infinityLog(N((1/3)ⁿ)) / Log(1/((1/3)ⁿ))

= lim_n->infinityLog(2ⁿ) / Log(3ⁿ)

= lim_n->infinity(nLog(2))/(nLog(3))

= Log(2)/Log(3) = 0.62989 ... .

Return to Box-Counting Dimension of the Cantor Set.

d_b	= lim_n->infinityLog(N((1/3)ⁿ)) / Log(1/((1/3)ⁿ))
	= lim_n->infinityLog(2ⁿ) / Log(3ⁿ)
	= lim_n->infinity(nLog(2))/(nLog(3))
	= Log(2)/Log(3) = 0.62989 ... .