where the initial condition parameter θ θ is given by θ θ = 1 π π sin − − 1 ⁡ ⁡ ( x 0 1 / 2 ) . For rational θ θ , after a finite number of iterations x n maps into a periodic sequence. But almost all θ θ are irrational, and, for irrational θ θ , x n never repeats itself – it is non-periodic. This solution equation clearly demonstrates the two key features of chaos – stretching and folding: the factor 2 shows the exponential growth of stretching, which results in sensitive dependence on initial conditions (the butterfly effect), while the squared sine function keeps x n folded within the range [0, 1].