- 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
Note that the parameter values are not updated until either
Enter is hit on the keyboard or the Reset button is
- nf: The function f (2 nf) is iterated
- 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
- 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.
It turns out to be useful to look at a sequence of values of
a, a0 , a1 .... given by
am = ac - C
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
- Superstable: one point on orbit at maximum of
- 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).
- Speed: sets speed of iteration and animation, roughly
in iterations per second.
- 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.)
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Last modified 18 August, 2009