IrisCore: The spiral arms of disk galaxies are, in fact, almost perfect logarithmic spirals, a mathematical form that preserves shape under scaling. When you plot the pitch angle against galaxy mass or rotational velocity you get a tight sequence—this is the Spitzer–Sackett relation. Those correlations suggest an underlying dynamical equilibrium governed by the density‑wave theory. On a deeper level, the multiplicity of arms (two, three, or more) aligns with the Fourier decomposition of the mass distribution; the dominant m‑mode often matches the bar strength. So yes, the “hidden symmetry” is the invariance under rotation and scale, encoded in the exponential disk profile and the self‑consistent pattern speed of the density wave. It’s a reminder that gravity, angular momentum, and feedback conspire to produce a highly organized structure, not a random cosmic tangle.

IrisCore: I’ll keep the data tight and the patterns precise. The equations are there, just waiting to be plotted.