Henon

Hénon map (M. Hénon, "A two-dimensional mapping with a strange attractor", 1976) — the example that showed a strange attractor needs neither a flow nor three dimensions, only a stretch and a fold. Zoom in anywhere on a filament and it resolves into more filaments: locally a line crossed with a Cantor set. Its Jacobian determinant is −b, so area contracts by exactly b every iterate no matter where you are.

x' = 1 − a·x² + y
y' = b·x

It opens running, on the model selector, with its own knobs. Rotate it by dragging, zoom with the wheel, and turn the parameters to see what the figure does when the system changes.