Fluid Mixing — Baker's Map & Horseshoe Chaos

Baker's map: Models chaotic advection in fluid mixing. Compress horizontally by λ, stretch vertically, fold back into unit square.
Equations: (x,y) ∈ [0,1)²: if y < λ → (x/2, y/λ); if y ≥ λ → (x/2+1/2, (y−λ)/(1−λ)).
Lyapunov exponent: σ = log(1/λ) > 0 (chaotic). KS entropy = σ. Every initial blob exponentially fills phase space.
Smale horseshoe: Baker's map is the prototypical horseshoe — stretching and folding generates a Cantor-set-like strange attractor (fractal mixing layers).
Fluid relevance: Chaotic advection (Aref 1984) — even simple laminar flows can mix chaotically. Lyapunov exponent determines mixing efficiency.