Using Mathematica software to graph Lissajous figures

Abstract

In this paper we look at the history and development of the so-called Lissajous figures. We show how to obtain the graphical representation of Lissajous figures in two and three dimensions, using Mathematica software. We show some of these figures, and the reader can modify the code to obtain any other figure. We also show how to build a simulation that shows the figure as a trajectory of a particle subjected to a restoring force in two or three dimensions. The simulation is output as a video in the format .avi, and the two examples chosen have been submitted to Youtube. Finally we give another alternative for building a simulation using Mathematica’s manipulate command. The latter comes out in the form of a box where we can manipulate all the desired parameters that influence the formation of different Lissajous figures.