The Logistic Map

From order to chaos

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Logistic map: $x \to rx(1 - x)$, a one-line population model.
• As r increases: a steady value, then cycles of 2, 4, 8…, then chaos (r ≳ 3.57).
• Chaos is deterministic, yet unpredictable in practice.

Steps

1. A simple population model
2. Steady state
3. A healthier population
4. Slow breeders
5. One step
6. Deterministic but unpredictable