# Manual

## Buttons

**Reset:** Sets the values of the parameters to those shown
in the boxes and reinitializes the plot (e.g. resets the initial
value to *x0*).
**Clear:** Clears the plot, but does not reset the
parameter values and maintains the current value of *x* .
**Step:** Performs and plots one step in the iteration.
**Start:** Starts repeated iteration and plotting with a
time between plotting set by the **delay** parameter (in ms).
**Clear** can be used while the iterations are proceeding if
the display becomes scrambled.
**Stop:** Stops the iteration and allows the parameters to
be updated.

## Text Boxes

Note that the parameter values are not updated until either
**Enter** is hit on the keyboard or the **Reset** button is
pushed.

**nf:** The function *f*^{ (2 nf}) is iterated
and plotted.
**nsc:** Rescaling parameter. The central portion of
*x* and *f* (i.e. near *x=0.5* are expanded by the
factor *(-2.502907875)*^{nsc}. The actual range of
*x* and *f* plotted are indicated as the "full scale" on
the plot.
**x0:** Initial value of *x* expressed as a fraction
of the range of the plot (i.e. involves the rescaling set by
**nsc** and **scale**).
**scale:** Further modifies the range of *x* and
*f* plotted by multiplying by the factor **scale** - again
indicated in the "full scale" shown on the plot. Useful for "fine
tuning" the plot.
**trans:** Sets the number of iterations done before values
are plotted. Useful to eliminate transient behavior if desired.
**a:** Sets the value of *a* in the maps. Value can be
typed in or set by the drop down box values below.

## Drop-down boxes

It turns out to be useful to look at a sequence of values of
*a*, *a*_{0} , a_{1} .... given by

a_{m} = a_{c} - C ^{
-m}

where *a*_{c} depends on the map function , but
= 4.6692016091... for all maps. The value of *m* can be
used to step through values of *a* yielding *2*^{m}
orbits (the symbol *I* in the list box for m corresponds to
infinity i.e. *a=a*_{c}). The value of *C* can be
chosen to give particular "types" of orbit.

The list boxes respectively:

- set the map to be iterated and
*a*_{c}
- set whether
*a > a*_{c} (**+**) or
*a < a*_{c} (**-**)
- set the value of
*C* giving values of *a*
corresponding to
**Superstable**: one point on orbit at maximum of
*f*.
**Instability**: cycle just unstable.
**Bandmerging**: chaotic bands merge in chaotic region
for *a > a*_{c}.

- set the value of
*m*

Values can also be typed directly into the text boxes (remember to
**Enter** or **Reset**).

## Scroll bar

**Speed:** sets speed of iteration and animation, roughly
in iterations per second.

## Mouse Click

**Clicking** the mouse within the plot area starts a new
iteration with an initial value given by the horizontal position.
(The vertical position has no effect.)

[Return to Home Page]

Last modified 18 August, 2009

Michael Cross