Experiment № 003 · The story
Strange Attractors
Why I picked it
This whole image is one point, moving. There are no thousands of particles and no grid of cells — just a single coordinate that gets fed back into a pair of equations over and over, a few hundred thousand times a second. Each new position is plotted as a faint speck. The "drawing" is simply the trail of where that one restless point has been. I wanted to build the purest version of an idea that has fascinated me since I first saw a printout of the Lorenz butterfly: that an utterly deterministic rule, with no randomness at all, can trace out a shape of endless, non-repeating intricacy.
What I enjoy about it
The form is a de Jong attractor — four numbers (a, b, c, d) define the whole universe of the picture. Nudge any one of them and the structure folds into something completely different: a wing, a knot, a cloud of filaments, a thing that looks woven. Because the same regions get visited far more often than others, I don't draw solid pixels — I accumulate density. Every visit adds a little light to a buffer, and the buffer is tone-mapped at the end, so the hot creases of the attractor glow and the rarely-touched edges fade to dust. Dragging slides you continuously through that four-dimensional parameter space, so you can fly between forms and watch one bleed into the next. Most of the shapes you'll find have never been seen by anyone — there are simply too many to ever enumerate.
Something you might take away
"Deterministic" and "predictable" are not the same word. The point never gets random input, yet you could never guess where it will be in ten thousand steps without actually running every step — and a microscopic change to a, b, c, or d sends it somewhere else entirely. That's the strange in strange attractor: the trajectory is pinned forever to this delicate fractal set, never settling, never repeating, never escaping. A lot of the world works like this — weather, heartbeats, traffic, crowds. Knowing the rule exactly is not the same as knowing the future.