Waggle Dance: Sun-Compass Transposition (3D)

Sun-Compass Transposition

Sun position (time of day) 135°

Distance scale 1.0 s/km

Recruit swarm size 40

Angle from gravity

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Run duration

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Decoded bearing

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Decoded distance

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How it works

Inside the dark hive, a scout dances on a vertical comb where gravity — not sunlight — is the only fixed reference. The straight "waggle run" points off from vertical by exactly the angle between the food's real compass bearing and the sun's current azimuth. A follower recovers the real bearing by adding the sun's live azimuth back onto that gravity-relative angle, then launches out through the hive entrance in that direction for a distance set by the run's duration (~1 s/km). Drag the sun-position slider: the same food source keeps its fixed real-world bearing, but the dance angle on the comb rotates to compensate, exactly as bees recalibrate through the day.

danceAngle  = bearing(food) − azimuth(sun)   [measured from gravity "up"]
flightBearing = danceAngle + azimuth(sun)     [recovered by the follower]
flightDistance = runDuration / scale

Sun position — the sun's azimuth in the outdoor scene; changing it rotates the required dance angle on the comb while the food marker itself never moves.
Distance scale — seconds of waggling per kilometre of real distance, ~1 s/km on average in real colonies.
Recruit swarm — an instanced group of followers that launches from the hive entrance each time the dance completes, tracing the transposed bearing out to the food marker.
Vibration rings — the substrate-borne pulses a waggle run sends through the comb, which is how nearby followers actually track the run in near-total darkness.

Dancer / waggle run Follower bee Recruit swarm Food source Sun

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