The Sierpinski curve, invented by
Waclaw Sierpinski, is
a
plane-filling, non-
intersecting fractal. It has the rather
odd properties of being
infinitely long, enclosing every
interior point in a
square, yet covering only 5/12 of
the
area of said square.
It looks like a recursively subdivided "knot", like this one:
/\___/\ /\___/\
\ / \ /
| | | |
| | | |
/ ___ \___/ ___ \
\/ \ / \/
| |
| |
/\___/ ___ \___/\
\ / \ /
| | | |
| | | |
/ ___ \ / ___ \
\/ \/ \/ \/