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## Remote Ready Biology Learning Activities

Remote Ready Biology Learning Activities has 50 remote-ready activities, which work for either your classroom or remote teaching.

# CHAOTIC DYNAMICAL SYSTEMS

### A presentation by Victor J. Donnay, Associate Professor of Mathematics, Bryn Mawr College, and students and colleagues at the College

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.

Java Applets by:
Derya Davis, Mathematics and Physics, Bryn Mawr College
Carin Ewing, Philosophy, Bryn Mawr College
Polygonal Billiards, Standard Map, Iteration Applet
Zhenjian He, Computer Science and Mathematics, Bryn Mawr College
Elliptic Billiards
Tina Shen, Computer Science, Bryn Mawr College
Polygonal Billiards, Staircase Game
Bogdan Butoi, Graduate Student in Mathematics, Bryn Mawr College
Victor Donnay, Associate Professor of Mathematics, Bryn Mawr College
Deepak Kumar, Assistant Professor of Computer Science, Bryn Mawr College

Supported in part by a grant to the College from the Howard Hughes Medical Institute.