Thirty thousand stars, each on its own clock

No shapes here, just two things: the curve of the arms and the speed of each star. The arms are a logarithmic spiral — the curve real galaxies actually wear, tighter as the pitch angle drops — and the stars are not drawn on that line, they are scattered around it. The speeds follow ω ∝ 1/r: fast on the inside, slow on the outside, which is what real galaxies measure. Drag the picture to tip the disc edge-on.

The slider this piece is really about is Shear. Turn it up and wait ten or twenty seconds: the old yellow-white stars get wound tighter and tighter by the difference between the fast inside and the slow outside, until the arms smear into a blur. That is the winding problem in astronomy — if the arms were a fixed set of stars, a few hundred million years would flatten them, and yet the galaxies we look at still have arms. So the arms are not a set of stars; they are a wave, and stars only pass through.
The blue young stars and pink HII regions are short-lived and ride with the wave, which is why they still mark the arms once the old ones have smeared. "Winding" changes the pitch angle of the spiral, and anything from 2 to 5 arms is worked out the same way.