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.