Equations
xn+1 = sin(a · yn) + c · cos(a · xn) yn+1 = sin(b · xn) + d · cos(b · yn)
The constants a, b, c, d (typically between –3 and 3) control the folding and stretching of phase-space, trapping the orbit on a fractal subset — a strange attractor.
Behaviour
Depending on parameter choice, the trajectory may:
- Collapse to a few simple loops
- Fill a ribbon-like band
- Or weave intricate, dust-fine lattices
Rendering Technique
- We iterate 2,000 points per animation frame.
- The first few thousand iterates are skipped to let the orbit settle on the attractor (transient removal).
- Each point is plotted as a 1×1 pixel rectangle — density builds brightness.
- Parameters randomise via New Parameters, selected from a curated list of aesthetically pleasing sets.
Related Attractors
The Clifford system is a simplified cousin of the Peter de Jong map. Many other two-dimensional iterated maps share similarly rich behaviour.