Gosper curve

The Gosper curve can also be used for efficient hierarchical hexagonal clustering and indexing.

The space filled by the curve is called the Gosper island.

The first few iterations of it are shown below: The Gosper Island can tile the plane.

In fact, seven copies of the Gosper island can be joined to form a shape that is similar, but scaled up by a factor of √7 in all dimensions.

Repeating this process indefinitely produces a tessellation of the plane.