Not necessarily a curve. You could have a 'square' spiral, or triangular, or a combination.

A spiral is a continuous section of line that circles around a central point, either inward or outward, but does not join itself. The line is often a hypothetical line, describing the path of an object or flow (see vortex).

It's a lot more interesting to try to specify what they can't do than what they can. Can you have a spherical spiral? Can you have a spiral in which the ends don't overlap on any plane? Can you spiral in 2 dimensions? How about 4? How chaotic can a spiral be before it stops being a spiral?

_{I was actually looking forward to trying to describe a spiral... Good job, arfarf.}