1xlyap(6x) XScreenSaver manual xlyap(6x)
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6 xlyap - display an array of Lyapunov exponents graphically
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9 xlyap [-BLps][-W width][-H height][-o filename][-a n ] [-b n ] [-w n ]
10 [-h n ] [-i xstart] [-M n ] [-R p ] [-S n ] [-D n ] [-F
11 string][-f string][-r n ] [-O n ] [-C n ] [-c n ] [-m n ] [-x
12 xpos] [-y ypos]
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15 xlyap generates and graphically displays an array of Lyapunov exponents
16 for a variety of iterated periodically forced non-linear maps of the
17 unit interval.
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20 -random A good choice for use with xscreensaver: picks random parame‐
21 ters from a built-in list.
22 -C n Specifies the minimum color index to be used for negative expo‐
24 nents
25 -D n Specifies the "dwell" or number of iterations over which to
27 average in order to calculate the Lyapunov exponent. Default is
28 50.
29 -H n Specifies the height of the window. Default is 256.
31 -L Indicates use log(x) + log(y) rather than log(xy).
33 -M r Specifies the real value to compare exponent values to for
35 indexing into a color wheel. The default value is 1.0.
36 -O n Specifies the minimum color index to be used for positive expo‐
38 nents
39 -R p Specifies pseudo-random forcing with probability p of using
41 parameter value 'a'.
42 -S n Specifies the "settle" or number of iterations prior to the
44 beginning of the calculation of the Lyapunov exponent. Default
45 is 50.
46 -a r Specifies the real value to use as the minimum parameter value
48 of the horizontal axis. Default is 2.0 for the logistic map.
49 -b n Specifies the real value to use as the minimum parameter value
51 of the vertical axis. Default is 2.0 for the logistic map.
52 -c n Selects one of six different color wheels to use. The default
54 color wheel is a rainbow palette.
55 -F 10101010
57 Specifies the "Function" forcing function to use. The example
58 above would alternate between iterating the circle and logistic
59 maps. An argument of "-F 2323" would alternate between left and
60 right logistic maps. The default is to only use the single
61 specified map (see the description of -m).
62 -f abbabaab
64 Specifies the forcing function to use. The default is to alter‐
65 nate between the "a" parameter and the "b" parameter.
66 -h r Specifies the real value to be used as the range over which the
68 vertical parameter values vary. The default is 1.0.
69 -i r Specifies the real value of the initial condition to use.
71 Default is 0.65.
72 -m n Selects between available non-linear maps of the unit interval.
74 A value of 0 specifies the logistic map. A value of 1, the cir‐
75 cle map. A value of 2, the left-logistic. A value of 3, the
76 right-logistic. A value of 4, the double-logistic. The default
77 is 0, the logistic map.
78 -o filename
80 Specifies the output filename to be used. If the -o option is
81 given, this file will automatically be written out at the com‐
82 pletion of the drawing. If it is not specified, a default
83 filename of lyap.out is used and only written if the 'f' or 'F'
84 keys are pressed during a run. The format of the output file is
85 PPM for color and PGM for monochrome. The parameters used to
86 calculate the picture are included as comments at the beginning
87 of the output file.
88 -p Switches color indices for negative and positive exponents.
90 Generally, causes negative exponents to be displayed in more
91 detail while darkening and narrowing the color range for posi‐
92 tive exponents. This can be toggled during runtime by pressing
93 the 'p' key.
94 -r n Specifies the maximum rgb value to be used. Default is 65000.
96 -s n Specifies the length of the color wheel spin.
98 -v Prints out the various values to be used and exits.
100 -w r Specifies the real value to be used as the range over which the
102 horizontal parameter values vary. The default is 1.0.
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107 During display, pressing any mouse button allows you to select the area
108 to be investigated with the mouse. The upper left hand corner of the
109 desired area is the location of the cursor when the button is pressed.
110 The lower right hand corner is specified by the cursor when the button
111 is released.
112 Use of the keys bBeEfFkKjJmnrRsSwWxXqQ indicates:
115 (<) Halve dwell value.
117 (>) Double dwell value.
118 ([) Halve settle value.
119 (]) Double settle value.
120 (B or b) Toggle button display on/off
121 (E or e) Recalculate the indices into the color wheel using a dif‐
122 ferent method
123 (F or f) Save current screen to ouput file (not yet implemented)
124 (H or h or ?) Display brief help message
125 (i) Decrement the interval between stripes for the striped color
126 map.
127 (I) Increment the interval between stripes for the striped color
128 map.
129 (K) Decrease value exponents are compared against by 0.05.
130 (J) Increase value exponents are compared against by 0.05.
131 (M) Decrease value exponents are compared against by 0.005.
132 (N) Increase value exponents are compared against by 0.005.
133 (m) Increment the map index, changing the map to be iterated.
134 (P or p) Toggle positive/negative exponent display.
135 (r) Redraw the window using previously calculated exponents.
136 (R) Redraw the window using the newly set dwell and/or settle val‐
137 ues.
138 (S) Spin the color wheel
139 (s) Halve the length of the spin and spin the color wheel
140 (u) Go up to the window just prior to the most recent zoom.
141 (U) Go all the way up to the original window.
142 (V or v) Display values of various parameters currently in use
143 (W or w) Use next color map.
144 (X or x) Clear window
145 (Q or q) quit
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150 Ronald Joe Record
151 The Santa Cruz Operation
152 P.O. Box 1900
153 Santa Cruz, CA 95061
154 rr@sco.com
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159 The algorithm was taken from the September 1991 Scientific American
160 article by A. K. Dewdney who gives credit to Mario Markus of the Max
161 Planck Institute for its creation. Additional information and ideas
162 were gleaned from the discussion on alt.fractals involving Stephen
163 Hall, Ed Kubaitis, Dave Platt and Baback Moghaddam. Assistance with
164 colormaps and spinning color wheels and X was gleaned from Hiram Claw‐
165 son. Rubber banding code was adapted from an existing Mandelbrot pro‐
166 gram written by Stacey Campbell.
167 Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.
169X Version 11 5.05-3 (06-Apr-2008) xlyap(6x)