A pulsar is a rotating neutron star whose magnetic axis is tilted by an angle α from the spin axis. Radio emission is beamed in a cone of half-width ρ around the magnetic axis, so we see a pulse once per rotation only if our line of sight, at angle ζ from the spin axis, is crossed by the cone. The angle γ between beam axis and line of sight obeys cos γ = cos α cos ζ + sin α sin ζ cos φ; the pulse lasts while γ < ρ, giving width cos ρ = cos α cos ζ + sin α sin ζ cos(W/2). The intensity profile used here is a simple Gaussian in γ.

Spin-down by magnetic dipole braking gives the standard estimates B ≈ 3.2×10¹⁹ √(P Ṗ) G, characteristic age τ = P/(2Ṗ) (assuming braking index 3 and a negligible birth period) and spin-down power Ė = 4π² I Ṗ / P³ with I = 10⁴⁵ g cm². The empirical beam width ρ ≈ 5.4°/√P (P in seconds) is a rough trend with large scatter. Example pulsar P and Ṗ values are rounded from published catalogue values.

Simplifications: a single cone (real beams are patchy and frequency dependent), no aberration, no gravitational light bending, no emission-height effects. The animation spins at a fixed visual rate, not the real period.