UPDATE: See Limaçons animating using SVG (Scalable Vector Graphics) and JavaScript

To see these figures, you must have Java turned on in your browser.

Limaçons (pronounced "leem-ah-sones") are produced by sine waves plotted in polar coordinates and sampled. The figures are aliasing artifacts of the sampling process. All of these figures are produced by varying four parameters: the sample rate (in samples per revolution), the frequency of the sine wave (in cycles per revolution), the number of revolutions, and a DC offset.

Click on the Random button to display a random Limaçon from a list of interesting ones. You can also type in your own parameters, or start with an existing Limaçon and modify one or more of the parameters. Try to discover the relationships between the parameters. If you discover any interesting Limaçons, mail me (

To change a field, click on the field you want to edit, and edit the value. When you hit ENTER your Limaçon will be displayed. The Samples and Loops parameters are integers, and the Freq and Offset parameters are floating point numbers.

View the java source for this applet.

View the java source for the applet that says hello on my home page.

Visit Wm's home page. Java is not just a language! See pictures from Java, as well as Bali, the incredible Galapagos Islands, Cuba, Antarctica, Africa, and other places.