I was perusing through Wikipedia and Wolfram in search of anything and everything related to fractals and chaos theory, and ran across the definition of a Standard Map. I have no freaking clue what it is all about, but apparently it is used “in the fields of mechanics of particles, accelerator physics, plasma physics, and solid state physics.” (so sayeth Wikipedia)
Anyway, it looked cool and the formula is pretty simple, so I did it in Flash. 🙂
[kml_flashembed movie=”http://www.bit-101.com/blog/wp-content/uploads/2008/01/standardmap.swf” width=”400″ height=”450″/]
Just click around, or switch on auto draw and drag around. The K slider adjusts one of the magic parameters that makes different kinds of pretty pictures. Too low and you’ll get a bunch of straight lines. Too high and you’ll get mostly television static. I also added some funky coloring based on the position you first click. Maybe I’ll make a larger version and market it as a techno album cover art generator.
I bet Jim Armstrong can tell us what it all means. 🙂
it kind of reminds me to those friendsofed flash books covers with Processing graphics. The one i hold now says to have a Henon phase diagram drawn by Bruce Tang (www.betaruce.com)
Yes, I know the ones you are talking about.
i must be easily impressed
or maybe just a big fan of techno album cover art generators
I really like this on auto draw
very neat
~S
Keith – I haven’t looked at chaos and nonlinear dynamics since about 1987. Bruce and Jared Tarbell have more background in this area. People interested in the topic can find lots of information online about basic maps, fixed points, and stability. The MathWorld article references a book by Rasband which is reputed to be quite good.
btw – I met Benoit Mandelbrot at a SIAM conference in 1986. Talked for a couple minutes, then he smiled and walked away with that look in his face that said “you pathetic simpelton.” In this field, I think he was correct 🙂 Really liked his work in financial analytics and the rescaled range method.
Keep up the great demos!
regards,
– jim
Could you could use this like Robert Hodgkins uses perlin noise? Getting random directions for wind or so?
Hello,
I don’t know if some one can give me some explications about the phase space of the Standard map of Chirikov, because i get it very difficult to explane it. So I’m writing the programm in Fortran Language and generate the figures by Mathlab. Now, I must make the explications of the differents figures.
If Some one can give somes information, this is my E-mail: jkebbab@yahoo.fr
Thinks .