1xlyap(6x)                     XScreenSaver manual                    xlyap(6x)
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NAME

6       xlyap - display an array of Lyapunov exponents graphically
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SYNOPSIS

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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DESCRIPTION

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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OPTIONS

21       -random A good choice for use with xscreensaver: picks  random  parame‐
22               ters from a built-in list.
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24       -C n    Specifies the minimum color index to be used for negative expo‐
25               nents
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27       -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.
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31       -H n    Specifies the height of the window. Default is 256.
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33       -L      Indicates use log(x) + log(y) rather than log(xy).
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35       -M r    Specifies the real value to  compare  exponent  values  to  for
36               indexing into a color wheel. The default value is 1.0.
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38       -O n    Specifies the minimum color index to be used for positive expo‐
39               nents
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41       -R p    Specifies pseudo-random forcing with  probability  p  of  using
42               parameter value 'a'.
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44       -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.
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48       -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.
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51       -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.
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54       -c n    Selects  one  of six different color wheels to use. The default
55               color wheel is a rainbow palette.
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57       -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).
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64       -f abbabaab
65               Specifies the forcing function to use. The default is to alter‐
66               nate between the "a" parameter and the "b" parameter.
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68       -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.
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71       -i r    Specifies the real value  of  the  initial  condition  to  use.
72               Default is 0.65.
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74       -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.
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80       -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.
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90       -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.
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96       -r n    Specifies the maximum rgb value to be used. Default is 65000.
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98       -s n    Specifies the length of the color wheel spin.
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100       -v      Prints out the various values to be used and exits.
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102       -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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NOTES

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.
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114
115       Use of the keys bBeEfFkKjJmnrRsSwWxXqQ indicates:
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117          (<) 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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AUTHOR

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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ACKNOWLEDGEMENTS

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.
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169       Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.
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173X Version 11               5.44-2.fc32 (16-Apr-2020)                 xlyap(6x)
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