In Dynamical Systems, an object moves according to a rule. Depending on the rule motion, the object may move in a regular fashion or in a chaotic fashion. We illustrate the ideas of chaos theory by letting the user play with three different types of dynamical systems:
1. Billiards in which a ball moves around inside a billiard table. The user can choose different shapes for the table (polygon, circle, ellipse, stadium). For some shapes, the billiard motion is regular; for others it is chaotic.
2. The Phase Space Game in which a point hops around inside a rectangle. The moving point produces beautiful colored patterns. The user can vary the rules of motion to produce either a regular pattern, a chaotic pattern or a pattern that has a mixture of regular and chaotic behaviour.
3. Iteration of a point on the real number line. A point moves on the number line according to various rules that the user chooses. One can display the motion either numerically or using the staircase method.