Chaotic Mixing — Baker Map & Fractal Invariant Set

The baker map (stretch + fold) is a paradigm of Hamiltonian chaos. Iterate blobs of dye to see fractal striations, or watch the invariant Cantor set form from repeller preimages.

Baker Map Parameters

Controls

Iterations n0
Lyapunov λ
Fractal dim d_f
Strips count
Baker Map:
(x,y) → (2x, y/2) if x<½
(x,y) → (2x−1, y/2+½) if x≥½

Lyapunov: λ = ln2 ≈ 0.693
After n steps: 2ⁿ vertical strips, width 2⁻ⁿ

Dissipative baker (a≠½): creates fractal attractor with d_f = 1 + ln2/ln(1/a) in one direction, Cantor set in the other.