In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations $x=A\sin(at+\delta)$, $y=B\sin(bt)$, which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857. By making $\delta=90$°, the equation for $x$ becomes: $x=A\cos(at)$. Furthermore making the scaling factors $A$ and $B$ a sine function of $t$, an astonishing variety of patterns results: