Lyapunov exponents: λ₁ = ln(1/λ), λ₂ = ln(λ). Area preserved: λ₁+λ₂ = 0. Chaotic for all λ ∈ (0,1).
Current distribution (n=0)
Density histogram
Folded baker: (x,y) → (2x mod 1, (y+⌊2x⌋)/2). The unit square is stretched horizontally, cut, and stacked.
Under iteration, initially-smooth distributions develop fractal microstructure — the signature of deterministic chaos.