Lorenz System

This simulation plots the solution of the Lorenz system of equations. The default initial conditions generate the well-known butterfly pattern.





Click the below button to restart the simulation with modified parameters


The Lorenz system is a set of ordinary differential equations originally studied by Edward Lorenz as a simplified model for atmospheric convection. Several of its solutions were known for their chaotic nature, wherein a small nudge to initial conditions changed the future course of the solution altogether. The mapping of one of these chaotic solutions (known as lorenz attractor) onto 3D space generates a trajectory akin to the wings of a butterfly. The term "butterfly effect" was coined from this uncanny resemblance. The equations are as follows:

\[ \frac{dx}{dt} = \sigma (y - x) \\ \frac{dy}{dt} = x(\rho - z) - y \\ \frac{dz}{dt} = xy - \beta z \\ \]


  1. A 3D, optimised and interactive version of the same simulation can be downloaded for the native environments for Windows and Linux from my GitHub
  2. Simulation may lag on lower-end devices.
  3. Work is being done to render the output in 3D
  4. Related: Double Pendulum, Conway's Game of Life, Planetary System

Developed by ChanRT | Fork me at GitHub