This is a local copy. The original can be found at

`http://www.lut.ac.uk/departments/ma/gallery/doubling`

used with permission from
Andy Burbanks

## Period Doubling## Interactive JAVA AppletProduced by Andy Burbanks |

This page requires a Java-enabled browser.

This Applet simulates graphical iteration of
the Logistic Map `f(x) = ax(1-x)`.

This
apparently simple function can display a whole range of
different behaviours when iterated (applied repeatedly to some
initial value of `x`).
The type of behaviour observed depends on the value of the
*parameter* `a`.

The
horizontal slider controls the initial point `x0`.
The vertical slider controls the parameter value `a`.
(Sliders can be operated by clicking and/or dragging.)
The final few iterations are shown in red to help detect
periodic orbits (cycles).

Shown below are some examples of the behaviour you should find.

The four plots show a 2-cycle, 4-cycle, 8-cycle, and ``chaos'', respectively.

Validated HTML3.2

Andy Burbanks

Mon 28 Oct 1996.