xlyap(6)

📦
version 6.15 · 2 versions
, in alpine 3.24, arch rolling, nixpkgs unstable

💖 xlyap(6) — the XScreenSaver manual, bestie edition 💖

okay so real talk: this is a page from the XScreenSaver manual, and it's all about xlyap, which is genuinely one of the prettiest little chaos-math toys in the whole suite. buckle up 🎀

✨ NAME ✨

xlyap — displays an array of Lyapunov exponents, but make it graphical 💅

🌸 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]
        [--fps] [--visual visual] [--window] [--root] [--window-id
        number]

🦋 DESCRIPTION 🦋

xlyap generates and then graphically displays an array of Lyapunov exponents — for a whole variety of iterated, periodically forced, non-linear maps of the unit interval. yes that's a lot of words. no we're not skipping any of them. it's giving math girl summer 🔥

👑 OPTIONS 👑

  • -random — honestly a great choice for xscreensaver duty: it just picks random parameters from a built-in list. lowkey the move 🫶
  • -C n — sets the minimum color index used for negative exponents.
  • -D n — the "dwell", aka the number of iterations you average over to actually calculate the Lyapunov exponent. default is 50.
  • -H n — window height, bestie. default is 256.
  • -L — tells it to use log(x) + log(y) instead of log(xy).
  • -M r — the real value that exponent values get compared against when indexing into a color wheel. default is 1.0.
  • -O n — sets the minimum color index used for positive exponents.
  • -R p — pseudo-random forcing, with probability p of using parameter value 'a'.
  • -S n — the "settle", aka the number of iterations before the Lyapunov exponent calculation even starts. default is 50.
  • -a r — the real value used as the minimum parameter value of the horizontal axis. default is 2.0 for the logistic map.
  • -b n — the real value used as the minimum parameter value of the vertical axis. default is 2.0 for the logistic map.
  • -c n — picks one of six different color wheels. default is a rainbow palette 🌈 (iconic, obviously).
  • -F 10101010 — the "Function" forcing function. in this example it'd alternate between iterating the circle and logistic maps. an argument of -F 2323 alternates between left and right logistic maps. the default is to only use the single specified map (peep the -m description below 👀).
  • -f abbabaab — the forcing function to use. default is to alternate between the "a" parameter and the "b" parameter.
  • -h r — the real value used as the range over which the vertical parameter values vary. default is 1.0.
  • -i r — the real value of the initial condition. default is 0.65.
  • -m n — chooses between the available non-linear maps of the unit interval:
    • 0 = the logistic map
    • 1 = the circle map
    • 2 = the left-logistic
    • 3 = the right-logistic
    • 4 = the double-logistic

default is 0, the logistic map.

  • -o filename — the output filename. if you give -o, this file gets automatically written out when the drawing completes. if you don't specify it, the default filename lyap.out is used, and it's only written if you press the 'f' or 'F' keys during a run. the output format is PPM for color and PGM for monochrome, and the parameters used to calculate the picture are included as comments at the beginning of the output file. organized queen 💅
  • -p — switches the color indices for negative and positive exponents. generally this makes negative exponents show up in more detail, while darkening and narrowing the color range for positive exponents. you can toggle this at runtime by pressing the 'p' key.
  • -r n — the maximum rgb value to use. default is 65000.
  • -s n — sets the length of the color wheel spin.
  • -v — prints out the various values that'll be used, then exits. a little "here's what I'm about to do" moment ✨
  • -w r — the real value used as the range over which the horizontal parameter values vary. default is 1.0.
  • --visual visual — specify which visual to use. legal values are the name of a visual class, or the id number (decimal or hex) of a specific visual.
  • --window — draw on a newly-created window. this is the default.
  • --root — draw on the root window.
  • --window-id number — draw on the specified window.

🎀 NOTES 🎀

while it's displaying, pressing any mouse button lets you select the area you wanna investigate with the mouse. the upper left hand corner of the desired area is wherever the cursor was when you pressed the button, and the lower right hand corner is wherever the cursor is when you release it. drag-to-zoom, basically 🖱️

use of the keys bBeEfFkKjJmnrRsSwWxXqQ does the following:

  • (<) Halve dwell value.
  • (>) Double dwell value.
  • ([) Halve settle value.
  • (]) Double settle value.
  • (B or b) Toggle button display on/off
  • (E or e) Recalculate the indices into the color wheel using a different method
  • (F or f) Save current screen to output file (not yet implemented)
  • (H or h or ?) Display brief help message
  • (i) Decrement the interval between stripes for the striped color map.
  • (I) Increment the interval between stripes for the striped color map.
  • (K) Decrease value exponents are compared against by 0.05.
  • (J) Increase value exponents are compared against by 0.05.
  • (M) Decrease value exponents are compared against by 0.005.
  • (N) Increase value exponents are compared against by 0.005.
  • (m) Increment the map index, changing the map to be iterated.
  • (P or p) Toggle positive/negative exponent display.
  • (r) Redraw the window using previously calculated exponents.
  • (R) Redraw the window using the newly set dwell and/or settle values.
  • (S) Spin the color wheel
  • (s) Halve the length of the spin and spin the color wheel
  • (u) Go up to the window just prior to the most recent zoom.
  • (U) Go all the way up to the original window.
  • (V or v) Display values of various parameters currently in use
  • (W or w) Use next color map.
  • (X or x) Clear window
  • (Q or q) quit
🫶 friendly reminder from the original page: (F or f) — save current screen to output file — is not yet implemented. so don't come for her when it doesn't save.

🌈 ENVIRONMENT 🌈

  • DISPLAY — to get the default host and display number.
  • XENVIRONMENT — to get the name of a resource file that overrides the global resources stored in the RESOURCE_MANAGER property.
  • XSCREENSAVER_WINDOW — the window ID to use with --root.

⭐ SEE ALSO ⭐

X(1), xscreensaver(1)

💜 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. 💀 (the word "viciously" is doing so much work here and I respect it)

and that's the whole page, bestie 🍓 — brought to you by X Version 11, version 6.15, dated 30-Mar-2026. slay, go stare at some exponents 💖✨

📦 where this page comes from