# 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, a0 , a1 .... given by

am = ac - C -m

where ac 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 2m orbits (the symbol I in the list box for m corresponds to infinity i.e. a=ac). The value of C can be chosen to give particular "types" of orbit.

The list boxes respectively:

• set the map to be iterated and ac
• set whether a > ac (+) or a < ac (-)
• 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 > ac.
• 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.)