Lorenz solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Lorenz equations

dxdt=σ(yx)dydt=x(ρz)ydzdt=xyβz.\begin{aligned} \dfrac{dx}{dt} &= \sigma (y-x) \\ \dfrac{dy}{dt} &= x (\rho - z) - y \\ \dfrac{dz}{dt} &= xy - \beta z. \end{aligned}

This system were first derived by Edward Lorenz and colleagues as a simplified mathematical model of atmospheric convection, although it can also arise in other fields. It is frequently used as an example of chaotic systems.

Simulation parameter form.
Parameter Value Explanation
Problem parameter
Problem parameter
Problem parameter
End time for the simulation in seconds (s)
Initial xx coordinate.
Initial yy coordinate.
Initial zz coordinate.
Error tolerance.
Tolerance type, can be either absolute (0) or relative (1).
Initial step size.
Minimum allowed step size.
Time increment for skipping ahead in animation.
Time you want to skip ahead to in animation when you press the skip button.
Width (in px) of Plotly windows used for plotting and animation below.
Height (in px) of Plotly windows used for plotting and animation below.
Proportion of animation time passed per real time. tScale=1.0t_{\mathrm{Scale}}=1.0 means animation and real time match. tScale<1.0t_{\mathrm{Scale}}<1.0 means the animation is going more slowly than real time. tScale>1.0t_{\mathrm{Scale}}>1.0 means it is going more rapidly.