The Equations
x_{n+1} = 1 − a x_n² + y_n
y_{n+1} = b x_n
For classic parameters a = 1.4 and b = 0.3, repeated iteration folds the plane into a fractal dust. Each pixel intensity in the demo corresponds to how many times the orbit visits that cell.
What to Look For
- Dense U-shaped bands indicating frequent visitation.
- Sparse regions that the orbit rarely explores.
- A colour gradient that slowly shifts each frame to highlight new paths.
Gallery Controls
- Click Reset to clear the canvas and randomise a, b.
- The demo plots 50 000 iterations per animation frame for speed.