Mathematica(@mathemetica ):Classic polar plot of the Butterfly Curve, generated from the equation r = exp(sin(t)) − 2 cos(4t) + sin((t − π/2)/12)^5 over t from 0 to 24π. This intricate closed curve creates a symmetric four-winged figure centered at the origin in the polar plane, highlighting the interplay of exponential growth, harmonic oscillation, and a modulated sine term.

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Mathematica@mathemetica

2026.05.14 03:34

Classic polar plot of the Butterfly Curve, generated from the equation r = exp(sin(t)) − 2 cos(4t) + sin((t − π/2)/12)^5 over t from 0 to 24π. This intricate closed curve creates a symmetric four-winged figure centered at the origin in the polar plane, highlighting the interplay of exponential growth, harmonic oscillation, and a modulated sine term.