Visualising maths

Lissajous figures

A simple Lissajous figure can be created using the parametric equations:

$$ \begin{align} x = sin(a t)\\ y = sin(b t) \end{align} $$

This animated graph shows how $x$ and $y$ vary with $t$ to create the curve. We are using $a = 3$ and $b = 2$:

The curve is cyclical. As $t$ varies from 0 to 2π radians, the curve traces a complete cycle and returns to the start point (0, 0). Increasing $t$ further will retrace the same curve.