The Logistic Map
A harmless formula where order collapses into chaos
Iterate xₙ₊₁ = r · xₙ · (1 − xₙ) and increase r. The fixed point splits into a 2-cycle, then 4, then 8 — a cascade of doublings that ends in full chaos around r ≈ 3.5699. Inside that cascade hides the Feigenbaum constant 4.6692…, the same number that governs unrelated chaotic systems across physics.
