LYAP(6X) LYAP(6X)
NAME
lyap - display an array of Lyapunov exponents graphically
SYNOPSIS
lyap [-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
lyap generates and graphically displays an array of Lyapunov exponents
for a variety of iterated periodically forced non-linear maps of the
unit interval.
OPTIONS
-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.
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LYAP(6X) LYAP(6X)
-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.
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LYAP(6X) LYAP(6X)
-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
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LYAP(6X) LYAP(6X)
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.
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