Strange Attractors

Strange attractors are interesting both mathematically and artistically. They are graphical representations of well defined mathematical functions that are highly sensitive to initial conditions. Many pages exist exhibiting pictures of strange attractors and other forms of chaos, but this little oasis of maths also presents you with films of strange attractors rotating in 3D space. And just when you thought maths couldn't get any more exciting!

These films are of a particular set of strange attractors; Pickover strange attractors, discovered by Clifford Pickover. They have been created with something I put together, then compressed using the DivX. If they don't play then you may need the DivX codec which can be downloaded via the links at the bottom of this page.

The Pickover class of strange attractors is generated with the following equations:

X(n) = sin(A * Y(n - 1)) - Z(n - 1) * cos(B * X(n - 1))
Y(n) = Z(n) * sin(C * X(n - 1)) - cos(D * Y(n - 1))
Z(n) = sin(X(n - 1))

The letters A to D are arbitrary constants that partially determine the end result. Even the smallest change in any of these constants can result in wildly different pictures.

Pictures

Download Films

I have only made a few so far, but here they are:
pickover01.avi 480x480, 20 seconds, DivX, 1.91 MB
pickover02.avi 480x480, 30 seconds, DivX, 2.79 MB
pickover03.avi 480x480, 30 seconds, DivX, 2.79 MB

Links

Pickover.com - Clifford Pickover's personal website.
Strange Attractors - at MathWorld
DivX - you may need to get the DivX codec from here in order to play the videos.