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Where chaos lives

Heat-map of the complex c-plane coloured by orbit period under one of three EML-family operators. Red = period 3 (Li-Yorke / Sharkovskii regime). Blue = period 1. Black = escape. Click anywhere to inspect the orbit at that c.

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palette — blue: period 1 · green: period 2 · red: period 3 (Sharkovskii) · yellow: period 4 · orange: 5-8 · purple: 9-32 · white: chaotic · black: escape

EXL is the outlier of the six exact-complete EML gates: a ~40 % red period-3 sea with period-6, period-12 doubling along its boundary — the overnight deep-session measured area ratios 4.60 / 4.44 / 4.45 between successive doublings, within 3.7 % of the classical Feigenbaum constant δ ≈ 4.669. Period 3 implies chaos of every order (Sharkovskii 1964, Li-Yorke 1975).