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:

/\___/\ /\___/\
\ / \ /
| | | |
| | | |
/ ___ \___/ ___ \
\/ \ / \/
| |
| |
/\___/ ___ \___/\
\ / \ /
| | | |
| | | |
/ ___ \ / ___ \
\/ \/ \/ \/