you know, that brings up another interesting question. Where does the corkscrew come from? It can't spring full-formed because that almost never happens in math. So how can you make it gradually appear?
You can't move the source point down through 0 and to 1, because that just makes it shrink and then come out as a line. *that* makes no sense. But - what if you rotate the source point around the imaginary axis?