3 xlyap \- display an array of Lyapunov exponents graphically
8 [-BLps][-W width][-H height][-o filename][-a
25 [-F string][-f string][-r
41 generates and graphically displays an array of Lyapunov exponents for a
42 variety of iterated periodically forced non-linear maps of the unit interval.
46 A good choice for use with xscreensaver: picks random parameters from
50 Specifies the minimum color index to be used for negative exponents
53 Specifies the "dwell" or number of iterations over which to average in order
54 to calculate the Lyapunov exponent. Default is 50.
57 Specifies the height of the window. Default is 256.
60 Indicates use log(x) + log(y) rather than log(xy).
63 Specifies the real value to compare exponent values to for indexing into
64 a color wheel. The default value is 1.0.
67 Specifies the minimum color index to be used for positive exponents
70 Specifies pseudo-random forcing with probability \fIp\fP of using parameter
74 Specifies the "settle" or number of iterations prior to the beginning of
75 the calculation of the Lyapunov exponent. Default is 50.
78 Specifies the real value to use as the minimum parameter value of the
79 horizontal axis. Default is 2.0 for the logistic map.
82 Specifies the real value to use as the minimum parameter value of the
83 vertical axis. Default is 2.0 for the logistic map.
86 Selects one of six different color wheels to use. The default color
87 wheel is a rainbow palette.
90 Specifies the "Function" forcing function to use. The example above would
91 alternate between iterating the circle and logistic maps. An argument of
92 "-F 2323" would alternate between left and right logistic maps. The default
93 is to only use the single specified map (see the description of -m).
96 Specifies the forcing function to use. The default is to alternate between
97 the "a" parameter and the "b" parameter.
100 Specifies the real value to be used as the range over which the vertical
101 parameter values vary. The default is 1.0.
104 Specifies the real value of the initial condition to use. Default is 0.65.
107 Selects between available non-linear maps of the unit interval. A value of
108 0 specifies the logistic map. A value of 1, the circle map. A value of 2,
109 the left-logistic. A value of 3, the right-logistic. A value of 4, the
110 double-logistic. The default is 0, the logistic map.
113 Specifies the output filename to be used. If the -o option is given, this
114 file will automatically be written out at the completion of the drawing.
115 If it is not specified, a default filename of lyap.out is used and only
116 written if the 'f' or 'F' keys are pressed during a run. The format of the
117 output file is PPM for color and PGM for monochrome. The parameters used to
118 calculate the picture are included as comments at the beginning of the output
122 Switches color indices for negative and positive exponents. Generally,
123 causes negative exponents to be displayed in more detail while darkening
124 and narrowing the color range for positive exponents. This can be toggled
125 during runtime by pressing the 'p' key.
128 Specifies the maximum rgb value to be used. Default is 65000.
131 Specifies the length of the color wheel spin.
134 Prints out the various values to be used and exits.
137 Specifies the real value to be used as the range over which the horizontal
138 parameter values vary. The default is 1.0.
142 During display, pressing any mouse button allows you to select the area to
143 be investigated with the mouse. The upper left hand corner of the desired
144 area is the location of the cursor when the button is pressed. The lower
145 right hand corner is specified by the cursor when the button is released.
148 \fIbBeEfFkKjJmnrRsSwWxXqQ\fP
152 (<) Halve dwell value.
154 (>) Double dwell value.
156 ([) Halve settle value.
158 (]) Double settle value.
160 (B or b) Toggle button display on/off
162 (E or e) Recalculate the indices into the color wheel using a different method
164 (F or f) Save current screen to output file (not yet implemented)
166 (H or h or ?) Display brief help message
168 (i) Decrement the interval between stripes for the striped color map.
170 (I) Increment the interval between stripes for the striped color map.
172 (K) Decrease value exponents are compared against by 0.05.
174 (J) Increase value exponents are compared against by 0.05.
176 (M) Decrease value exponents are compared against by 0.005.
178 (N) Increase value exponents are compared against by 0.005.
180 (m) Increment the map index, changing the map to be iterated.
182 (P or p) Toggle positive/negative exponent display.
184 (r) Redraw the window using previously calculated exponents.
186 (R) Redraw the window using the newly set dwell and/or settle values.
188 (S) Spin the color wheel
190 (s) Halve the length of the spin and spin the color wheel
192 (u) Go up to the window just prior to the most recent zoom.
194 (U) Go all the way up to the original window.
196 (V or v) Display values of various parameters currently in use
198 (W or w) Use next color map.
200 (X or x) Clear window
207 The Santa Cruz Operation
215 The algorithm was taken from the September 1991 Scientific American article
216 by A. K. Dewdney who gives credit to Mario Markus of the Max Planck Institute
217 for its creation. Additional information and ideas were gleaned from the
218 discussion on alt.fractals involving Stephen Hall, Ed Kubaitis, Dave Platt
219 and Baback Moghaddam. Assistance with colormaps and spinning color wheels
220 and X was gleaned from Hiram Clawson. Rubber banding code was adapted from
221 an existing Mandelbrot program written by Stacey Campbell.
223 Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97.