# Lorenz system > [[PORTAL_Complex_system|Complex system]] · [[PORTAL_Dynamical_system|Dynamical system]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Lorenz_system.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Lorenz system — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> The Lorenz system is a set of three coupled nonlinear ordinary differential equations, derived by meteorologist Edward Lorenz in 1963 as a drastically simplified model of atmospheric convection. Despite having just three variables and three parameters, the system is capable of chaotic behaviour: trajectories that never repeat or settle down, yet remain bounded within a distinctive butterfly-shaped region of phase space known as the Lorenz attractor. ## Overview This build renders trajectories through the system's three-dimensional phase space live, with the three governing parameters — conventionally named sigma, rho, and beta — adjustable directly, so the transition from stable equilibrium to periodic orbit to full chaos can be watched as a continuous change rather than read as an equation. Small changes to the starting point produce wildly diverging trajectories after only a short time — the sensitive dependence on initial conditions behind the popular "butterfly effect" metaphor, and the founding example of what is now called a [[Dynamical_system|dynamical system's]] strange attractor. The Lorenz system remains the standard first example of deterministic chaos: fully deterministic equations, zero randomness anywhere, and yet long-term prediction is impossible in practice — a core motivating case for [[Chaos_theory|chaos theory]]. **On the spine:** [[Dynamical_system]] · [[Complex_system]] · [[Chaos_theory]] · [[Phase_space]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Lorenz_system) : [Wikitube](https://en.wikitube.io/wiki/Lorenz_system) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*