NAME

       xlyap - display an array of Lyapunov exponents graphically

SYNOPSIS

       xlyap [-BLps] [-W width] [-H height] [-o filename] [-a n] [-b n] [-w n] [-h n] [-i xstart]
               [-M n] [-R p] [-S n] [-D n] [-F string] [-f string] [-r n] [-O n] [-C  n]  [-c  n]
               [-m  n]  [-x  xpos]  [-y  ypos]  [--fps]  [--visual  visual]  [--window]  [--root]
               [--window-id number]

DESCRIPTION

       xlyap generates and graphically displays an array of Lyapunov exponents for a  variety  of
       iterated periodically forced non-linear maps of the unit interval.

OPTIONS

       -random A  good  choice for use with xscreensaver: picks random parameters from a built-in
               list.

       -C n    Specifies the minimum color index to be used for negative exponents

       -D n    Specifies the "dwell" or number of iterations over which to average  in  order  to
               calculate the Lyapunov exponent. Default is 50.

       -H n    Specifies the height of the window. Default is 256.

       -L      Indicates use log(x) + log(y) rather than log(xy).

       -M r    Specifies  the  real value to compare exponent values to for indexing into a color
               wheel. The default value is 1.0.

       -O n    Specifies the minimum color index to be used for positive exponents

       -R p    Specifies pseudo-random forcing with probability p of using parameter value 'a'.

       -S n    Specifies the "settle" or number of iterations  prior  to  the  beginning  of  the
               calculation of the Lyapunov exponent. Default is 50.

       -a r    Specifies  the  real value to use as the minimum parameter value of the horizontal
               axis. Default is 2.0 for the logistic map.

       -b n    Specifies the real value to use as the minimum parameter  value  of  the  vertical
               axis. Default is 2.0 for the logistic map.

       -c n    Selects  one  of  six  different color wheels to use. The default color wheel is a
               rainbow palette.

       -F 10101010
               Specifies the  "Function"  forcing  function  to  use.  The  example  above  would
               alternate between iterating the circle and logistic maps. An argument of "-F 2323"
               would alternate between left and right logistic maps. The default is to  only  use
               the single specified map (see the description of -m).

       -f abbabaab
               Specifies the forcing function to use. The default is to alternate between the "a"
               parameter and the "b" parameter.

       -h r    Specifies the real value to be used as the range over which the vertical parameter
               values vary. The default is 1.0.

       -i r    Specifies the real value of the initial condition to use. Default is 0.65.

       -m n    Selects  between  available  non-linear  maps  of  the unit interval. A value of 0
               specifies the logistic map. A value of 1, the circle map. A value of 2, the  left-
               logistic. A value of 3, the right-logistic. A value of 4, the double-logistic. The
               default is 0, the logistic map.

       -o filename
               Specifies the output filename to be used. If the -o option  is  given,  this  file
               will  automatically be written out at the completion of the drawing.  If it is not
               specified, a default filename of lyap.out is used and only written if the  'f'  or
               'F'  keys are pressed during a run. The format of the output file is PPM for color
               and PGM for monochrome. The parameters used to calculate the picture are  included
               as comments at the beginning of the output file.

       -p      Switches  color  indices  for  negative  and positive exponents. Generally, causes
               negative exponents to be displayed in more detail while  darkening  and  narrowing
               the  color  range  for  positive  exponents. This can be toggled during runtime by
               pressing the 'p' key.

       -r n    Specifies the maximum rgb value to be used. Default is 65000.

       -s n    Specifies the length of the color wheel spin.

       -v      Prints out the various values to be used and exits.

       -w r    Specifies the real value to be  used  as  the  range  over  which  the  horizontal
               parameter values vary. The default is 1.0.

       --visual visual
               Specify  which visual to use.  Legal values are the name of a visual class, or the
               id number (decimal or hex) of a specific visual.

       --window
               Draw on a newly-created window.  This is the default.

       --root  Draw on the root window.

       --window-id number
               Draw on the specified window.

NOTES

       During display, pressing any mouse button allows you to select the area to be investigated
       with  the  mouse.  The  upper  left hand corner of the desired area is the location of the
       cursor when the button is pressed. The lower right hand corner is specified by the  cursor
       when the button is released.

       Use of the keys bBeEfFkKjJmnrRsSwWxXqQ indicates:

          (<) Halve dwell value.
          (>) Double dwell value.
          ([) Halve settle value.
          (]) Double settle value.
          (B or b) Toggle button display on/off
          (E or e) Recalculate the indices into the color wheel using a different method
          (F or f) Save current screen to output file (not yet implemented)
          (H or h or ?) Display brief help message
          (i) Decrement the interval between stripes for the striped color map.
          (I) Increment the interval between stripes for the striped color map.
          (K) Decrease value exponents are compared against by 0.05.
          (J) Increase value exponents are compared against by 0.05.
          (M) Decrease value exponents are compared against by 0.005.
          (N) Increase value exponents are compared against by 0.005.
          (m) Increment the map index, changing the map to be iterated.
          (P or p) Toggle positive/negative exponent display.
          (r) Redraw the window using previously calculated exponents.
          (R) Redraw the window using the newly set dwell and/or settle values.
          (S) Spin the color wheel
          (s) Halve the length of the spin and spin the color wheel
          (u) Go up to the window just prior to the most recent zoom.
          (U) Go all the way up to the original window.
          (V or v) Display values of various parameters currently in use
          (W or w) Use next color map.
          (X or x) Clear window
          (Q or q) quit

ENVIRONMENT

       DISPLAY to get the default host and display number.

       XENVIRONMENT
               to  get  the name of a resource file that overrides the global resources stored in
               the RESOURCE_MANAGER property.

       XSCREENSAVER_WINDOW
               The window ID to use with --root.

SEE ALSO

       X(1), xscreensaver(1)

AUTHOR

       Ronald Joe Record
       The Santa Cruz Operation
       P.O. Box 1900
       Santa Cruz, CA 95061
       rr@sco.com

ACKNOWLEDGEMENTS

       The algorithm was taken from the September 1991  Scientific  American  article  by  A.  K.
       Dewdney  who  gives  credit  to Mario Markus of the Max Planck Institute for its creation.
       Additional information  and  ideas  were  gleaned  from  the  discussion  on  alt.fractals
       involving  Stephen  Hall,  Ed  Kubaitis,  Dave Platt and Baback Moghaddam. Assistance with
       colormaps and spinning color wheels and X was gleaned from Hiram Clawson.  Rubber  banding
       code was adapted from an existing Mandelbrot program written by Stacey Campbell.

       Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.