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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]

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  ran-
             dom 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 400.

     -B      Causes the stop, go, spin and  quit  buttons  to  be
             displayed.

     -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 200.

     -W n    Specifies the width of the window. Default is 256.

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

     -b n    Specifies the real  value  to  use  as  the  minimum
             parameter value of the vertical axis. Default is 3.0
             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 logis-
             tic 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 0.05.

     -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 monochrom. The  parame-
             ters  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 nar-
             rowing  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 35000.

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

     -u      Produces a usage message.

     -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.

     -x n    Specifies the x  screen  coordinate  of  the  window
             (default is 256).

     -y n    Specifies the y  screen  coordinate  of  the  window
             (default is 256).



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  ouput  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



AUTHOR
             Ronald Joe Record
          The Santa Cruz Operation
               P.O. Box 1900
            Santa Cruz, CA 95061
                 [email protected]



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.  Addi-
     tional  information  and ideas were gleaned from the discus-
     sion 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 Claw-
     son.  Rubber  banding code was adapted from an existing Man-
     delbrot program written by Stacey Campbell.

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

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