x ← r·x·(1−x), a single line, and inside it live both order and chaos. For r below 3 the population settles on one equilibrium wherever it starts; past 3 it alternates between two levels, then four, then eight, each doubling costing an interval of r about 4.669 times shorter than the last — the Feigenbaum constant, which recurs in countless other systems. Beyond 3.57 lies chaos, yet in the middle of the chaotic band a period-3 window opens near r = 3.83, and magnifying any small branch reveals the whole diagram again.
x ← r·x·(1−x), a single line, and inside it live both order and chaos. For r below 3 the population settles on one equilibrium wherever it starts; past 3 it alternates between two levels, then four, then eight, each doubling costing an interval of r about 4.669 times shorter than the last — the Feigenbaum constant, which recurs in countless other systems. Beyond 3.57 lies chaos, yet in the middle of the chaotic band a period-3 window opens near r = 3.83, and magnifying any small branch reveals the whole diagram again.
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