Parties are a frequent occurrence in a college town
. Some parties get "out of hand"
, attracting guests the hosts couldn't possibly have invited. During my own college years, I attended many a party. I was even invited to some of them.
It was at one such party that I happened to glance across the room and spot a girl sporting straws shoved onto her top incisor
s, resembling huge fangs. I knew she was the girl for me.
..Oh wait, that's not right.
You are probably aware of ordinary attractor
s, resulting from the indefinite iteration
of an operation within a space
. Some of the series thus generated converge to a single point, a fixed-point attractor
. Other sequences go for awhile then cycle among a finite set of points, a limit cycle
Many do nothing like that, and that is why they are interesting.
Some operations never repeat themselves, even when iterated infinitely. The series of points resulting from iteration does not even resemble a Cauchy Sequence
, that is, the series does not get closer and closer to a final limit point
How can you consider something this strange
"? Simply put, the sequence confines itself to a compact subspace
of the space in question.
The Lorenz attractor
, resulting from a few differential equations modeling convection, is the archetypal strange attractor.
The Sierpinski Triangle
can be considered another, resulting from a geometric algorithm iterated indefinitely.
s and the Mandelbrot Set
are also strange attractors, residues after iterating the entire complex number space an infinite number of times.
We have Floris Takens and David Ruelle to thank for this term.
However, examples of strange attractors were discovered well before even Lorenz. They were considered mathematical "monstrosities" and avoided whenever possible. It was only with the advent of computers that mathematician
s were able to discover these objects' beautiful, strange attraction.