Can One Equation Weave Butterfly Wings?

BEHIND THE WORK

Can one equation weave butterfly wings?

One point follows r(t) = exp(cos t) − 2 cos(4t) + sin⁵(t/12), with x(t) = r(t) sin t and y(t) = r(t) cos t, for 0 ≤ t ≤ 24π. The fast terms shape the wing loops. The slow sin⁵(t/12) term changes successive passes, adding inner and outer layers instead of tracing the same outline. Here exp(u) means e raised to the power u; r is a signed radial factor, so negative values place the point in the opposite direction. The full interval makes twelve parameter turns and closes the path.

This is a planar butterfly curve, not the Lorenz attractor or a simulation of a real butterfly.

Artismathic turns equations into visual art—one function at a time.

Curve reference: https://mathworld.wolfram.com/ButterflyCurve.html Music: 'Eternal Garden' by Dan Henig

#MathArt #GenerativeArt #ButterflyCurve