This illustrates the fact that the projection from the helix to
the annulus is a covering map. For each sufficiently small patch
in the annulus, the preimage in the helix is a disjoint union of a
discrete set of homeomorphic patches. This is essentially the
same as the behaviour of the exponential map $\exp\colon B\to A$,
where
\begin{align*}
B &= \{ x + iy \in \mathbb{C} \;|\; 1 < x < 2 \} \\
A &= \{ z \in \mathbb{C} \;|\; e < |z| < e^2 \}.
\end{align*}
You can click and drag the patch, or use the mouse wheel to change the size of the patch.