Pascal's Triangle can be used to generate artistic geometric patterns. To do so, choose a remainder. For each number in the triangle, shade that number a different colour for each different remainder. The applet below allows you to try this. For best results, use a modulus between 2 and 16.

To try a different modulus, enter the modulus in the text box, either below or above the display on the left.

Technical note: One of two versions will load on the left: An HTML5 canvas version for modern browers, or a Java-based applet for older browsers that support Java.

View source code for Java applet

If you like this sort of content, you may want to check out other interactive content on Math Lair.

Try this applet for a few different moduli and see if you notice any interesting patterns in the designs. For example, the designs produced by prime numbers are simpler than those produced by composite numbers.

Sources used (see bibliography page for titles corresponding to numbers): 38.