ChaosMaster allows you to graphically view the behaviour of a chaotic system.
It is the simplest one I know of and it is k times x squared -1, repeated (iterated) by plugging the result back into the equation. It displays all the classic symptoms of chaos:
• Doubling cascades (Bifircation)
• Sensitivity to initial conditions (The butterfly effect)

You can adjust k by using the graphical slider on the right of the panel OR by typing a value directly into the k display box. As the value of k increases the system heads towards a chaotic state, following a period doubling cascade between 1.24 and 1.41. This is probably the most interesting area to study. (And at around 1.75 - weird)
The twelve most recent values of x are shown under history.
If you get a bit bored waiting for the period to settle down, hit one of the iterate buttons to 'suddenly' perform either 100 or 1000 iterations. These will not be plotted graphically.