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 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 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 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 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 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 0.05.
-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-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 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 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.
