Lissajous curves were studied by the French physicist and mathematician Jules Antoine Lissajous (1822 - 1880). Lissajous curves are the composition of two harmonic motions (sinusoids):

x = amplitude * cos ( frequency1 * time )
y = amplitude * cos ( frecuency2 * time + phase ) The shape of the curves are highly sensitive to the ratio frequency1/frequency2. Do experiment with different values of the frequencies and the phase using the fields provided in the simulation.