Peano Plane
The Peano Plane, a.k.a. the space-fitting curve, is a curving line that fills an entire two dimensional plane. If devised correctly, the line is able to fill the plane without coming to a dead end, or intersecting itself.
Structures exhibiting this characteristic includ human brains and coral reefs. The structures are extremely good at utilizing available space.
Further Reading
- Wikipedia: Space-filling Curve