XLYAP(6X)
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]
DESCRIPTION
xlyap generates and graphically displays an array of Lya-
punov 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 Lya-
punov exponent. Default is 400.
-B Causes the stop, go, spin and quit buttons to be
displayed.
-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 val-
ues 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 200.
-W n Specifies the width of the window. Default is 256.
-a r Specifies the real value to use as the minimum
parameter value of the horizontal axis. Default is
3.0 for the logistic map.
-b n Specifies the real value to use as the minimum
parameter value of the vertical axis. Default is
3.0 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 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 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 0.05.
-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-logis-
tic. 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
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 n Specifies the maximum rgb value to be used.
Default is 35000.
-s n 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 r Specifies the real value to be used as the range
over which the horizontal parameter values vary.
The default is 1.0.
-x n Specifies the x screen coordinate of the window
(default is 256).
-y n Specifies the y screen coordinate of the window
(default is 256).
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 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
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.