--- /dev/null
+
+
+
+XLYAP(6X) XLYAP(6X)
+
+
+N\bNA\bAM\bME\bE
+ xlyap - display an array of Lyapunov exponents graphically
+
+S\bSY\bYN\bNO\bOP\bPS\bSI\bIS\bS
+ _\bx_\bl_\by_\ba_\bp [-BLps][-W width][-H height][-o filename][-a _\bn ] [-b
+ _\bn ] [-w _\bn ] [-h _\bn ] [-i xstart] [-M _\bn ] [-R _\bp ]
+ [-S _\bn ] [-D _\bn ] [-F string][-f string][-r _\bn ] [-O
+ _\bn ] [-C _\bn ] [-c _\bn ] [-m _\bn ] [-x xpos] [-y ypos]
+
+D\bDE\bES\bSC\bCR\bRI\bIP\bPT\bTI\bIO\bON\bN
+ _\bx_\bl_\by_\ba_\bp generates and graphically displays an array of Lya-
+ punov exponents for a variety of iterated periodically
+ forced non-linear maps of the unit interval.
+
+O\bOP\bPT\bTI\bIO\bON\bNS\bS
+ -random A good choice for use with xscreensaver: picks
+ random parameters from a built-in list.
+
+ -C _\bn Specifies the minimum color index to be used for
+ negative exponents
+
+ -D _\bn Specifies the "dwell" or number of iterations over
+ which to average in order to calculate the Lya-
+ punov exponent. Default is 400.
+
+ -B Causes the stop, go, spin and quit buttons to be
+ displayed.
+
+ -H _\bn Specifies the height of the window. Default is
+ 256.
+
+ -L Indicates use log(x) + log(y) rather than log(xy).
+
+ -M _\br Specifies the real value to compare exponent val-
+ ues to for indexing into a color wheel. The
+ default value is 1.0.
+
+ -O _\bn Specifies the minimum color index to be used for
+ positive exponents
+
+ -R _\bp Specifies pseudo-random forcing with probability _\bp
+ of using parameter value 'a'.
+
+ -S _\bn Specifies the "settle" or number of iterations
+ prior to the beginning of the calculation of the
+ Lyapunov exponent. Default is 200.
+
+ -W _\bn Specifies the width of the window. Default is 256.
+
+ -a _\br Specifies the real value to use as the minimum
+ parameter value of the horizontal axis. Default is
+ 3.0 for the logistic map.
+
+ -b _\bn Specifies the real value to use as the minimum
+
+
+
+ 1
+
+
+
+
+
+XLYAP(6X) XLYAP(6X)
+
+
+ parameter value of the vertical axis. Default is
+ 3.0 for the logistic map.
+
+ -c _\bn Selects one of six different color wheels to use.
+ The default color wheel is a rainbow palette.
+
+ -F _\b1_\b0_\b1_\b0_\b1_\b0_\b1_\b0
+ Specifies the "Function" forcing function to use.
+ The example above would alternate between iterat-
+ ing 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 sin-
+ gle specified map (see the description of -m).
+
+ -f _\ba_\bb_\bb_\ba_\bb_\ba_\ba_\bb
+ Specifies the forcing function to use. The default
+ is to alternate between the "a" parameter and the
+ "b" parameter.
+
+ -h _\br Specifies the real value to be used as the range
+ over which the vertical parameter values vary. The
+ default is 1.0.
+
+ -i _\br Specifies the real value of the initial condition
+ to use. Default is 0.05.
+
+ -m _\bn 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-logis-
+ tic. A value of 4, the double-logistic. The
+ default is 0, the logistic map.
+
+ -o _\bf_\bi_\bl_\be_\bn_\ba_\bm_\be
+ 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 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 _\bn Specifies the maximum rgb value to be used.
+ Default is 35000.
+
+
+
+ 2
+
+
+
+
+
+XLYAP(6X) XLYAP(6X)
+
+
+ -s _\bn 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 _\br Specifies the real value to be used as the range
+ over which the horizontal parameter values vary.
+ The default is 1.0.
+
+ -x _\bn Specifies the x screen coordinate of the window
+ (default is 256).
+
+ -y _\bn Specifies the y screen coordinate of the window
+ (default is 256).
+
+
+
+N\bNO\bOT\bTE\bES\bS
+ 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 _\bb_\bB_\be_\bE_\bf_\bF_\bk_\bK_\bj_\bJ_\bm_\bn_\br_\bR_\bs_\bS_\bw_\bW_\bx_\bX_\bq_\bQ 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.
+
+
+
+ 3
+
+
+
+
+
+XLYAP(6X) XLYAP(6X)
+
+
+ (P or p) Toggle positive/negative exponent display.
+ (r) Redraw the window using previously calculated expo-
+ nents.
+ (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
+
+
+
+A\bAU\bUT\bTH\bHO\bOR\bR
+ Ronald Joe Record
+ The Santa Cruz Operation
+ P.O. Box 1900
+ Santa Cruz, CA 95061
+ rr@sco.com
+
+
+
+A\bAC\bCK\bKN\bNO\bOW\bWL\bLE\bED\bDG\bGE\bEM\bME\bEN\bNT\bTS\bS
+ 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.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ 4
+
+
projects / xscreensaver / blobdiff