<Dl> <Dd> x n + 1 = 4 x n (1 − x n), 0 ≤ x 0 ≤ 1, (\ displaystyle x_ (n + 1) = 4x_ (n) (1 - x_ (n)), \ quad 0 \ leq x_ (0) \ leq 1,) </Dd> </Dl> <Dd> x n + 1 = 4 x n (1 − x n), 0 ≤ x 0 ≤ 1, (\ displaystyle x_ (n + 1) = 4x_ (n) (1 - x_ (n)), \ quad 0 \ leq x_ (0) \ leq 1,) </Dd> <P> which, unlike most chaotic maps, has a closed - form solution: </P> <Dl> <Dd> x n = sin 2 ⁡ (2 n θ π) (\ displaystyle x_ (n) = \ sin ^ (2) (2 ^ (n) \ theta \ pi)) </Dd> </Dl>

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