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

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HENWARP Documentation



       henwarp - warps a square into the phase space of the Henon


       henwarp -help
              [-width  integer]  [-height  integer] [-swap] [-len
              integer] [-count integer] [-A double]  [-B  double]
              [-ulx  double]  [-uly  double] [-lly double] [-inv]
              [-mag integer] [-term string]


       A square (initially centered about the origin)  is  trans-
       formed  by  the  Henon  system,  which is described by the
       equation x(t+1) = A - x(t)^2 + B * x(t - 1), a fixed  num-
       ber of times according to the specified parameters.


       -width integer
              Width of the plot in pixels.

       -height integer
              Height of the plot in pixels.

       -swap  Swap the x and y axis.

       -len integer
              Length of edge of square.

       -count integer
              Number of transformations.

       -A double
              Value of the A parameter.

       -B double
              Value of the B parameter.

       -ulx double
              Upper-left corner x-coordinate.

       -uly double
              Upper-left corner y-coordinate.

       -lly double
              Lower-left corner y-coordinate.

       -inv   Invert all colors?

       -mag integer
              Magnification factor.

       -term string
              How to plot points.


       You  may wish to try this with a small length for the size
       of square and watch how the resulting plot changes as  you
       slowly  increase  the  value  passed  to the -count option
       starting at zero.   The square will slowly spread out  and
       converge to the attractor of the system.

       The  method  for  choosing  the  viewable  region may seem
       counter-intuitive at first, but it has some  nice  proper-
       ties.   In  particular, selecting the exact (x, y) coordi-
       nates for the upper-left corner  and  only  selecting  the
       lower right y coordinate forces both the x and y scales to
       be identical since all scales are uniquely  determined  by
       these values along with the plot width and height.  If you
       then change the width or height of the plot, the  relative
       scales  will still match up.  The options for making a box
       work similarly.


       The length of the square is in pixels and works best if it
       is an odd value.  With even numbered values it can produce
       a gap in the plot  for  small  values  supplied  with  the
       -count option.

       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