2. B. Box-Counting Dimension

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

Covering the product of the Cantor set snd line interval with smaller and smaller boxes, we see the patterns illustrated in the table below the picture.

N(1/3) = 6 = 31⋅21 N(1/9) = N((1/3)2) = 36 = 9⋅4 = 32⋅22   and in general   N((1/3)n) = 3n⋅2n.

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