Lorenz IFS - movies
Important Note: if you want to link, please link to this page. PLEASE do not link directly to the movies.
It applies especially to users of the StumbleUpon toolbar, if you like or dislike movies thumbup or thumbdown this page, not movie files themselves.
If you link directly to the movies, i will have to take movies down and put movies on youtube in much lower quality. In which case your links will break anyway. I had to do it before.
Thanks for your cooperation.
Equations:
Dx=a*(Pyn-Pxn)
Dy=b*Pxn-Pyn-Pxn*Pzn
Dz=Pxn*Pyn-c*Pzn
L=s*D*1/sqrt(Dx2+Dy2+Dz2)
Pn+1=Pn+L


a=10 b=28 c=2.6666 s=0.1 to 10, spins 360 degrees around while morphing from s=0.1 to s=10. File is 1024x768 mpeg4 avi, encoded using lavc, is 4.1MB big


Comments: It starts with plain Lorenz attractor. As value of s increases, interesting patterns begin to form. At larger values of s, it sometimes goes over stable cycle solutions, when the chaotic distribution pattern collapses to set of points (it looks bit like blinking of broken fluorescent lightbulb).


a=10 b=20 c=3 s=10.01, spin 360 degrees clockwise if you look from above. File is 1024x768 mpeg4 avi, encoded using lavc, is 1.5MB big


Comments: Just spin around, constant parameters.


Another movie, with a=10 b=28 c=2.6666 s=0.1 to 28 , note: file is 7.1mb big. Looks very good, nice ending.

Sources (C++) of the program used to render these movies:
lorenz_ifs_movie_2006-11-10-r1.tar.gz (Released under zlib license.)
Warning: code quality is somewhat poor, that's weekend hack-job. It's written for Linux, you'll probably need porting to run it on non-unix systems (see the system() calls). Requirements: ImageMagick with Magick++ .

I will add more movies to this page soon as i explore the parameters space.

If you can't view the movies you can try using VLC media player.

By the way, "Lorenz IFS" (Lorenz Iterated Function System) it is the name i gave to this chaotic attractor that i have discovered when experimenting with modifications of the Lorenz attractor. I have no idea if somebody discovered it before me. (also, if by chance you want to call it Lorenz-Lavrov or something like that i won't mind it much either ;-) heh. )

(C) 2004..2013 Dmytry Lavrov.
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