A quadratic map is a quadratic recurrence equation of the form x_(n + 1) = a_2 x_n^2 + a_1 x_n + a_0. While some quadratic maps are solvable in closed form (for example, the three solvable cases of the logistic map), most are not. A simple example of a quadratic map with a closed-form solution is x_n = x_(n - 1)^2 with x_0 = 2, which has solution x_n = 2^(2^n), the first few terms of which for n = 0, 1, ... are 2, 4, 16, 256, 65536, 4294967296, ... (OEIS A001146).

Bogdanov map | Hénon map | Julia set | linear recurrence equation | logistic map | Lozi map | Mandelbrot set | quadratic | quadratic equation | quadratic formula | quadratic recurrence equation | recurrence equation | strange attractor | Sylvester's sequence