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

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MG Documentation



       mg - plot the phase space of the Mackey-Glass system


       mg -help
       mg     [-width  integer] [-height integer] [-skip integer]
              [-points integer] [-delta integer]  [-tau  integer]
              [-A  double]  [-B double] [-dt double] [-x0 double]
              [-factor  double]  [-data]  [-inv]  [-mag  integer]
              [-term string]


       The  phase  space  of  the  Mackey-Glass  system, which is
       described by the delay differential equation

       dx(t)/dt = A * x(t-Tau) / (1 + x(t-Tau)^10) - B * x(t),

       is plotted according to the specified parameters.  The  x-
       coordinate  of the plot is determined by x(t) while the y-
       coordinate is determined by x(t-delta).


       -width integer
              Width of the plot in pixels.

       -height integer
              Height of the plot in pixels.

       -skip integer
              Number of initial points to skip.

       -points integer
              Number of points to plot.

       -delta integer
              Time steps to delay for.

       -tau integer
              Value of the Tau parameter.

       -A double
              Value of the A parameter.

       -B double
              Value of the B parameter.

       -dt double
              Time step size.

       -x0 double
              Initial X value.

       -factor double
              Auto-scale expansion factor.

       -data  Don't plot, but print points.

       -inv   Invert all colors?

       -mag integer
              Magnification factor.

       -term string
              How to plot points.


       The plot region is determined by the points that are  ini-
       tially  skipped.  If this number is too small (i.e., it is
       not very representative of the range of the  plotted  val-
       ues),  then  you may need to increase the number specified
       by the -skip option.  Alternatively, you  can  adjust  the
       value   given   to   -factor,  which  simply  fractionally
       increases the border of the plot.

       The program uses a second-order Euler's method to  perform
       the  numerical integration, which is sufficient for simple
       tasks such as this.


       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