Lissajous curves. In mathematics, a Lissajous curve, also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations 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. The visual form of these curves is often suggestive of a three-dimensional knot.