Provided by: xscreensaver-data_5.36-1ubuntu1_amd64 bug

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]

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.

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

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.