ReadMe file for Cycles version 1.02 (07-Mar-1992)
by Stuart McDonald

This application draws a graph showing the period-
doubling of the logistic map equation

x    = r x (1-x )
 n+1      n    n

The user chooses minimum and maximum values for
lambda (the "r" in the equation above) and the
number, n, of iterations to be performed.
The machine then iterates the equation n times for
each value of lambda between the two values you
gave, with lambda being shown on the horizontal
axis.
  x  is given the value 0.5, and the result of
   0

each iteration is plotted on the vertical axis.  The
first few iterations are plotted in dark grey, and
subsequent iterations are plotted in successively
brighter shades, so that the values closest to any
fixed points (if there are any) are plotted in
white.  Chaos can be seen when the period doubling
becomes critical, at around lambda = 3.6

If you have any comments/suggestions/tips/
improvements, please write to me at the
following address:

Stuart McDonald
"Maple House"
1, Bursledon Road
Hedge End
Southampton
SO3 4BP
ENGLAND

This program is PD; see the Legal file for
more information on that side of things.





  As they always say, if this scrolled by too quickly for
  you, load Edit and try again.  Or, I suppose, you could
  learn to read very, very quickly.



