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]
13 [-fps]
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16 xlyap generates and graphically displays an array of Lyapunov exponents
17 for a variety of iterated periodically forced non-linear maps of the
18 unit interval.
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21 -random A good choice for use with xscreensaver: picks random parame‐
22 ters from a built-in list.
23 -C n Specifies the minimum color index to be used for negative expo‐
25 nents
26 -D n Specifies the "dwell" or number of iterations over which to
28 average in order to calculate the Lyapunov exponent. Default is
29 50.
30 -H n Specifies the height of the window. Default is 256.
32 -L Indicates use log(x) + log(y) rather than log(xy).
34 -M r Specifies the real value to compare exponent values to for
36 indexing into a color wheel. The default value is 1.0.
37 -O n Specifies the minimum color index to be used for positive expo‐
39 nents
40 -R p Specifies pseudo-random forcing with probability p of using
42 parameter value 'a'.
43 -S n Specifies the "settle" or number of iterations prior to the
45 beginning of the calculation of the Lyapunov exponent. Default
46 is 50.
47 -a r Specifies the real value to use as the minimum parameter value
49 of the horizontal axis. Default is 2.0 for the logistic map.
50 -b n Specifies the real value to use as the minimum parameter value
52 of the vertical axis. Default is 2.0 for the logistic map.
53 -c n Selects one of six different color wheels to use. The default
55 color wheel is a rainbow palette.
56 -F 10101010
58 Specifies the "Function" forcing function to use. The example
59 above would alternate between iterating the circle and logistic
60 maps. An argument of "-F 2323" would alternate between left and
61 right logistic maps. The default is to only use the single
62 specified map (see the description of -m).
63 -f abbabaab
65 Specifies the forcing function to use. The default is to alter‐
66 nate between the "a" parameter and the "b" parameter.
67 -h r Specifies the real value to be used as the range over which the
69 vertical parameter values vary. The default is 1.0.
70 -i r Specifies the real value of the initial condition to use.
72 Default is 0.65.
73 -m n Selects between available non-linear maps of the unit interval.
75 A value of 0 specifies the logistic map. A value of 1, the cir‐
76 cle map. A value of 2, the left-logistic. A value of 3, the
77 right-logistic. A value of 4, the double-logistic. The default
78 is 0, the logistic map.
79 -o filename
81 Specifies the output filename to be used. If the -o option is
82 given, this file will automatically be written out at the com‐
83 pletion of the drawing. If it is not specified, a default
84 filename of lyap.out is used and only written if the 'f' or 'F'
85 keys are pressed during a run. The format of the output file is
86 PPM for color and PGM for monochrome. The parameters used to
87 calculate the picture are included as comments at the beginning
88 of the output file.
89 -p Switches color indices for negative and positive exponents.
91 Generally, causes negative exponents to be displayed in more
92 detail while darkening and narrowing the color range for posi‐
93 tive exponents. This can be toggled during runtime by pressing
94 the 'p' key.
95 -r n Specifies the maximum rgb value to be used. Default is 65000.
97 -s n Specifies the length of the color wheel spin.
99 -v Prints out the various values to be used and exits.
101 -w r Specifies the real value to be used as the range over which the
103 horizontal parameter values vary. The default is 1.0.
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108 During display, pressing any mouse button allows you to select the area
109 to be investigated with the mouse. The upper left hand corner of the
110 desired area is the location of the cursor when the button is pressed.
111 The lower right hand corner is specified by the cursor when the button
112 is released.
113 Use of the keys bBeEfFkKjJmnrRsSwWxXqQ indicates:
116 (<) Halve dwell value.
118 (>) Double dwell value.
119 ([) Halve settle value.
120 (]) Double settle value.
121 (B or b) Toggle button display on/off
122 (E or e) Recalculate the indices into the color wheel using a dif‐
123 ferent method
124 (F or f) Save current screen to output file (not yet implemented)
125 (H or h or ?) Display brief help message
126 (i) Decrement the interval between stripes for the striped color
127 map.
128 (I) Increment the interval between stripes for the striped color
129 map.
130 (K) Decrease value exponents are compared against by 0.05.
131 (J) Increase value exponents are compared against by 0.05.
132 (M) Decrease value exponents are compared against by 0.005.
133 (N) Increase value exponents are compared against by 0.005.
134 (m) Increment the map index, changing the map to be iterated.
135 (P or p) Toggle positive/negative exponent display.
136 (r) Redraw the window using previously calculated exponents.
137 (R) Redraw the window using the newly set dwell and/or settle val‐
138 ues.
139 (S) Spin the color wheel
140 (s) Halve the length of the spin and spin the color wheel
141 (u) Go up to the window just prior to the most recent zoom.
142 (U) Go all the way up to the original window.
143 (V or v) Display values of various parameters currently in use
144 (W or w) Use next color map.
145 (X or x) Clear window
146 (Q or q) quit
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151 Ronald Joe Record
152 The Santa Cruz Operation
153 P.O. Box 1900
154 Santa Cruz, CA 95061
155 rr@sco.com
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160 The algorithm was taken from the September 1991 Scientific American
161 article by A. K. Dewdney who gives credit to Mario Markus of the Max
162 Planck Institute for its creation. Additional information and ideas
163 were gleaned from the discussion on alt.fractals involving Stephen
164 Hall, Ed Kubaitis, Dave Platt and Baback Moghaddam. Assistance with
165 colormaps and spinning color wheels and X was gleaned from Hiram Claw‐
166 son. Rubber banding code was adapted from an existing Mandelbrot pro‐
167 gram written by Stacey Campbell.
168 Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.
170X Version 11 5.43-2.fc31 (27-Aug-2019) xlyap(6x)