Stretching and folding creates exponential mixing: a hallmark of chaotic fluid dynamics
Step: 0 | Stretching factor: 1.00
The baker map stretches the unit square horizontally by 1/λ, compresses vertically, then cuts and stacks — mimicking a baker kneading dough. Mathematically: (x,y) → (x/λ, λy) for x < λ, and (x,y) → ((x−λ)/(1−λ), λy+(1−λ)) otherwise. After n iterations, filaments have width λⁿ → 0, demonstrating exponential stretching with Lyapunov exponent γ = −ln(λ). This is the simplest model of chaotic advection — the same mechanism that mixes cream into coffee or pollutant dispersal in fluids. Left: particle positions. Right: phase-space density (brightness = log density).