Dung Beetle Skylight Polarization Compass 2D: Sky Map & Menotaxis Arena

This is the 2D companion to the 3D dome sim: the same Rayleigh single-scattering optics and the same menotaxis steering law, computed independently in two genuinely 2D representations rather than a flattened camera view. The top panel is an azimuthal-equidistant polar projection of the sky -- the zenith at the center, the horizon at the rim -- with the degree of polarization and e-vector orientation recomputed at every map point and projected onto the disc's own radial/tangential axes. The bottom panel is a true top-down arena: a beetle rolling a dung ball only ever moves in the horizontal plane, so its bearing-holding behavior is already native 2D motion. Adjust sun elevation and cloud cover to watch the polarization map brighten or wash out, trigger a fresh orientation dance, or knock the beetle off course and watch it re-dance and steer back -- with heading noise that scales directly against how much polarization signal the sky actually offers.