Provided by: xscreensaver-data-extra_5.11-1ubuntu2_i386 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 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
                   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.