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xlyap(6)		      XScreenSaver manual		      xlyap(6)

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 av-
	       erage  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  in-
	       dexing 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 pa-
	       rameter value 'a'.

       -S n    Specifies the "settle" or number	of iterations prior to the be-
	       ginning 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.  De-
	       fault 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 ar-
       ticle 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.

X Version 11		      5.12 (15-Sep-2010)		      xlyap(6)

NAME | SYNOPSIS | DESCRIPTION | OPTIONS | NOTES | AUTHOR | ACKNOWLEDGEMENTS

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