Every star here orbits the galactic center on a nearly circular path, but — unlike a solar system — it does not obey Kepler's law where outer objects orbit much slower. Beyond a small central bulge, this model's rotation curve is flat: circular speed v(r) stays roughly constant with radius, matching what astronomers actually measure in real spiral galaxies and the strongest indirect evidence for dark matter (visible mass alone predicts speeds that fall off at large radius; they don't).
A flat rotation curve still means differential rotation: angular speed ω(r) = v(r)/r, so inner stars — smaller r — sweep around far faster in angle per year than outer stars, even though their linear speed is the same. Set pitch to a modest value and watch: stars start on straight radial spokes, and pure ω(r) shear alone winds them into a trailing spiral within a few core periods, no separate "arm force" required.
The pitch slider adds a seed logarithmic-spiral offset (like the 3D version's initial branch geometry) on top of that rotation; scatter jitters each star's radius/angle at spawn so the arms look grainy rather than perfectly combed, matching real stellar disks. Toggle rotation off to freeze the frame and inspect the instantaneous arm shape.