/sci/ - Science & Math

Are there any easy to visualize homeomorphisms from the sphere to itself with a single fixed point?
Consider [math]f: \mathbb{R}^2 \rightarrow \mathbb{R}^2[/math] defined by [math]f(x, y) = (x+1, y)[/math]. [math]f[/math] has no fixed points, obviously.
Since the Alexandroff one-point compactification is a functor [math]AOP[/math] (name invented right now, there's probably something else that's used more often)(see wikipedia for a source) we can get [math]AOP(f): S^2 \rightarrow S^2[/math], which is a homeomorphism and only fixes the point at infinity.

But this example is super fucking jarring, I want something cuter.