We present a catalog of 64 spiral phenomena spanning 12 domains of science — from quantum spin (10u207b³u2075 m) to cosmic filament rotation (10²u2076 m). Three equations describe all observed instances: the logarithmic spiral r = ae^(bθ), Fibonacci packing at the golden angle θu2099 = n × 137.508°, and angular momentum conservation L = Iω. No free parameters are introduced beyond the growth rate b, which varies by scale. The same functional form appears across quantum mechanics, atomic structure, chemistry, biology, neuroscience, Earth science, planetary dynamics, stellar evolution, galactic structure, cosmology, multiverse models, and pure mathematics. We argue this is not metaphor but mechanism: spin is the only behavior available to energy in a rotational spacetime. The catalog was assembled without targeted search; a systematic survey would likely expand it. All source code for interactive visualizations is included.