Equations · equation
Lorenz System
Nonlinear Dynamics · 1963
- Equation
- ẋ = σ(y−x) · ẏ = x(ρ−z) − y · ż = xy − βz
- Field
- Nonlinear Dynamics
- Named After
- Edward Lorenz
- Year
- 1963
Symbols
x, y, z the state of a drastically simplified convecting atmosphere · σ, ρ, β knobs for the fluid's properties · the dots are time derivatives
Significance
Three innocuous-looking equations whose solutions never settle and never repeat, tracing the butterfly-shaped attractor that named an effect: Lorenz found that rounding a starting value in the fourth decimal produced a different weather forecast entirely. Deterministic yet unpredictable — the discovery that killed Laplace's demon.
Referenced by
equation
theory
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.