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

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PHASE1D Documentation



       phase1d - plot phase-space of a one-dimensional map


       phase1d -help
              [-width  integer]  [-height integer] [-points inte-
              ger] [-skip integer] [-r double] [-aux double] [-x0
              double]   [-dx  double]  [-func  string]  [-arrows]
              [-inv] [-mag integer] [-term string]


       A phase-space diagram is plotted for a one-dimensional map
       according to the specified options.  If the option for -dx
       is non-zero, then two trajectories are plotted: one  star-
       ing  at  x0, and the other starting at (x0 + dx).  See the
       MAPS section of the manual page for details of  what  maps
       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.

       -points integer
              Number of points to plot.

       -skip integer
              Number of points to skip.

       -r double
              Value for r.

       -aux double
              Auxiliary map parameter.

       -x0 double
              Initial value for x.

       -dx double
              Difference for second trajectory.

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

              Show arrows to indicate directions?

       -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