attractor viewer
This attractor Viewer was made with Processing.
The attractor viewer can be used to make movies like these: a a Lorenz, a Lorenz 84 and the other of a de Jong attractor.
I’ve also put up some nice wallpaper sized images on Flickr.
An attractor is a set of rules upon a number of variables (dimensions) that, after time, can either converge to a point, diverge to
infinity or follow some strange trajectory. An attractor is deterministic, meaning that it’s state at a certain point in time can only be calculated by iterating toward that point in time.
There is a nice anecdote about this. The University of Stockholm (Sweden) held a contest. He who finds a way to predetermine the position of three planets in any given point in time (the three body problem) would win 2500 crones and a gold medal.
In January, 1889, the entry that was declared the winner was that of the French mathematician Jules Henri Poincaré. He was invited to Sweden to collect his prize.
But shortly after (in the middle of the printing for the first publication) Poincar� found an error in his calculations. The three body problem was unsolvable after all.
This also shows how something seemingly simple as a planet and two moons can actually be a chaotic system.
Simplicity is also one of the beautifull properties of strange attractors. For example the Lorenz attractor is this:
xx = x + e*( (-a*x*d) + (a*y*d) )
yy = y + e*( ( b*x*d) – (y*d) – (z*x*d) )
zz = z + e*( (-c*z*d) + (x*y*d) )
resulting in this:
