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.
(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.