## Chaos Visualization

Chaos theory is a mathematical theory dealing with dynamic systems that are highly sensitive to initial conditions.The following visualization is called a logistic map. We take the function x

_{n+1}= rx

_{n}(1-x

_{n}) and perform iterations starting with some x

_{0}between 0 and 1.

After performing enough iterations, several behaviors may be observed:

- The value of the function will be 0.
- The value of the function will diverge.
- The value of the function will converge to a single value.
- The value of the function will oscillate between a set of possible values.
- The value of the function will be chaotic - no oscillations can be detected.

The interesting region in which the function converges is between r=-2 and r=4.

To use the applet, enter the start and end values for 'r' and click "Draw".

The logistic map shows the convergence values x

_{n}for different values of 'r'.