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.

在本文中，我们研究了所谓的 Lissajous 图形的历史和发展。我们展示了如何使用 Mathematica 软件获得二维和三维 Lissajous 图形的图形表示。我们展示了其中的一些图，读者可以修改代码以获得任何其他图。我们还展示了如何构建一个模拟，将图形显示为在二维或三个维度上受到恢复力的粒子的轨迹。模拟输出为.avi格式的视频，选择的两个例子已经提交给Youtube。最后，我们提供了另一种使用 Mathematica 的操作命令构建模拟的替代方法。后者以一个盒子的形式出现，我们可以在其中操纵影响不同 Lissajous 图形形成的所有所需参数。