Cantor Set Explorer

Move the Depth slider to generate stages of the Cantor set. Use the mouse-wheel to zoom and drag to pan. Watch the total length shrink as (2/3)n.

5
Depth nSegments 2nTotal length (2/3)n

Box-Counting Dimension Lab

Choose an integer k to partition the unit interval into boxes of length 1/3k. Count how many boxes intersect the Cantor set, then plot log N(s) vs log (1/s) to estimate the box dimension.

4
s = 1/34 ≈ 0.0123 N(s) = 20
ks = 1/3kN(s)