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XLYAP !!!XLYAP NAME SYNOPSIS DESCRIPTION OPTIONS NOTES AUTHOR ACKNOWLEDGEMENTS ---- !!NAME xlyap - display an array of Lyapunov exponents graphically !!SYNOPSIS ''xlyap'' [[-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 ''xlyap'' generates and graphically displays an array of Lyapunov exponents for a variety of iterated periodically forced non-linear maps of the unit interval. !!OPTIONS -random A good choice for use with xscreensaver: picks random parameters from a built-in list. -C ''n'' Specifies the minimum color index to be used for negative exponents -D ''n'' Specifies the -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 -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. -F ''10101010'' Specifies the -f ''abbabaab'' Specifies the forcing function to use. The default is to alternate between the -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. -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: ( !!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. Viciously hacked for xscreensaver by Jamie Zawinski, 20-Nov-97. ----
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