The Computational Beauty of Nature
Computer Explorations of Fractals, Chaos,
Complex Systems, and Adaptation

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BIFUR1D Documentation



       bifur1d - plot bifurcations from a one-dimensional map


       bifur1d -help
              [-width  integer] [-height integer] [-skip integer]
              [-rmin double] [-rmax double] [-func string] [-fac-
              tor  double]  [-ymin  double]  [-ymax double] [-aux
              double] [-box integer] [-brmin double] [-brmax dou-
              ble]  [-bymin  double] [-bymax double] [-inv] [-mag
              integer] [-term string]


       A bifurcation diagram is plotted for a one-dimensional map
       according  to  the specified options.  In general, the map
       is iterated for several different values of the 'r' param-
       eter  so  that  the  long  term behavior of the map can be
       observed as a function of  are  supported.   User  defined
       maps  can  be  added  to  the  file maps1d.c, but you must
       recompile the program.


       -width integer
              Width of the plot in pixels.

       -height integer
              Height of the plot in pixels.

       -skip integer
              Number of initial points to skip.

       -rmin double
              Smallest value for r.

       -rmax double
              Largest value for r.

       -func string
              Map function to use (one of 'log',  'tent',  'sin',
              or 'gauss').

       -factor double
              Multiplicative factor for number of iterates.

       -ymin double
              Smallest value for y range.

       -ymax double
              Largest value for y range.

       -aux double
              Auxiliary map parameter.

       -box integer
              Line width for a box.

       -brmin double
              Smallest r-value for the box.

       -brmax double
              Largest r-value for the box.

       -bymin double
              Smallest value for box y range.

       -bymax double
              Largest value for box y range.

       -inv   Invert all colors?

       -mag integer
              Magnification factor.

       -term string
              How to plot points.


       The following four one-dimensional maps are allowed:

       Logistic Map:
              x(t+1) = 4 * r * x(t) * (1.0 - x(t))

       Tent Map:
              x(t+1) = (x(t) <= 0.5) ? 2 * r * x(t) : 2r * (1.0 -

       Sine Map:
              x(t+1) = sin(x(t) * PI * aux * 2 * r) / 2 + 0.5

       Gaussian Map:
              x(t+1) = r * exp(-aux * (x(t)  -  0.5)  *  (x(t)  -

       See  the  file  "maps1d.c"  to see how to add user-defined


       No sanity checks are performed to make sure  that  any  of
       the options make sense.


       Copyright (c) 1997, Gary William Flake.

       Permission  granted  for any use according to the standard
       GNU ``copyleft'' agreement provided that the author's com-
       ments  are  neither  modified nor removed.  No warranty is
       given or implied.
Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002