Real night-flying moths (and many other insects) navigate by transverse orientation: they hold a fixed angle α between their flight heading and the direction of the brightest light source, rather than steering straight at it. The moon sits so far away that its rays arrive effectively parallel everywhere in the scene — so holding a constant angle to it produces ordinary straight-line compass flight, which is the whole point of the strategy.
A nearby lamp breaks that assumption: its direction keeps changing as the moth moves, because it is a point source, not a source "at infinity". Holding the same fixed angle α to a point source instead produces a mathematically inevitable logarithmic (equiangular) spiral that tightens inward — the same shape you get from a pursuit curve. This is the leading physical explanation for why moths circle lamps and streetlights instead of flying past them.
Each moth blends the two references by relative brightness: w = I_lamp / (I_lamp + I_moon), with I_lamp ∝ brightness / distance² (inverse-square falloff) and I_moon fixed. Far from the lamp, moonlight dominates (w→0, straight flight); close to the lamp, it dominates instead (w→1, spiraling capture). Turn rate limits how fast a moth's heading can chase that target bearing, matching a real animal's finite steering speed.
- α (bearing angle) — near 0° the moth flies almost straight at the lamp; larger α widens the spiral.
- Lamp brightness — raises I_lamp, so the point-source rule takes over from farther away.
- Turn rate — low values produce loose, wandering spirals; high values track the ideal spiral tightly.