Box-Counting Dimension of a Line Segment
Covering a line segment with smaller and smaller boxes we see the pattern in the table on the right.
N(1)
= 1
N(1/2)
= 2 =
1/(1/2)
N(1/4)
= 4 =
1/(1/4)
N(1/8)
= 8 =
1/(1/8)
and so in general
N(r)
=
1/r.
Return to
Box-Counting Dimension
.