Cantor set


last updated: 20050107 
George Cantor (18451918) constructed the Cantor set.
The curve is a base motif
fractal which uses a line segment as base. The motif is to divide the line
segment into three equal parts and replace the middle:
The fractal dimension of the Cantor set is equal to log2/log3, what is about
0.6309 ^{1)}.
The Cantor set can be generalized to a motif where the middle section 1  2a is
omitted.
Then the fractal dimension is equal to log2/log(1/a).
The Sierpinski curve is a twodimensional variant on
the Cantor set.
The Menger sponge is a threedimensional variant on
the Cantor set.
notes
1) Fractal dimension = log N / log e, where N is the number of line segments
and e the magnification.
For the Cantor set: N=2, e=3. 