Swallow Curve

mathsolver (53)in #art • 6 years ago

A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity.

A typical harmonograph has two pendulums that move in such a fashion, and a pen that is moved by two perpendicular rods connected to these pendulums. Therefore, the path of the harmonograph figure is described by the parametric equations

$\begin{align*} x(t) = A_1 \sin (f_1 t + p_1) e^{-d_1t} + A_2 \sin(f_2 t + p_2) e^{-d_2 t} \\ y(t) = A_3 \sin (f_3 t + p_3) e^{-d_3t} + A_4 \sin(f_4 t + p_4) e^{-d_4 t} \end{align*}$

The swallow curve has parameters