This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Lorenz equations: \[ \begin{aligned} \dfrac{dx}{dt} &= \sigma (y-x) \\ \dfrac{dy}{dt} &= x (\rho - z) - y \\ \dfrac{dz}{dt} &= xy - \beta z. \end{aligned} \]