The Lemniscate Motion Occurs Naturally in the Flapping of Birds

Short Answer

The lemniscate motion occurs naturally in the flapping of birds' wings. The bird's vertical lift and wing sweep create the distinctive figure-eight pattern. The patterns vary with the different wing profiles. Compare the two possible lemniscate patterns by graphing them on the same polar graph: r² = cos 2θ and r² = cos (2θ + 1).