Provided by: xscreensaver-data_5.08-0ubuntu3_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  parame-
                ters from a built-in list.
 
        -C n    Specifies the minimum color index to be used for negative expo-
                nents
 
        -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 expo-
                nents
 
        -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 alter-
                nate 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 cir-
                cle  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  com-
                pletion  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  posi-
                tive  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 dif-
        ferent 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  val-
        ues.
           (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  Claw-
        son.  Rubber  banding code was adapted from an existing Mandelbrot pro-
        gram written by Stacey Campbell.
 
        Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.