This image plots the graph of the function y = cos(ksin(x)) over the range of x from 0 to pi and as we vary k we get a moving picture.

When k = 0 this gives the graph of y = 1 which is a straight line, and we then let k vary from 0 to 15 and back again to 0.

This is one of the figures ones sees on a cathode ray tube when one puts different frequency signals on to the "x and y plates".

The formula for the curve is x = cos(5 t), y = cos(4 t) where t runs from 0 to 2pi and then back to 0 again.

These curves were studied by the French mathematician Jules Antoine Lissajous (1822 to 1880).