The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed temperature difference Δ T, under gravity g, with buoyancy α, thermal diffusivity κ, and kinematic viscosity ν. The full equations are d/(dt)( del ^2 ϕ) | = | (dψ)/(dz) d/(dx)( del ^2 ψ) - (dψ)/(dx) d/(dz)( del ^2 ψ) + (ν del )^2( del ^2 ψ) + g α(d T)/(d x) (dT)/(dt) | = | (dT)/(dz) (dψ)/(dx) - (dθ)/(dx) (dψ)/(dz) + (κ del )^2 T + (Δ T)/H (dψ)/(dx).

butterfly effect | Lorenz equations | Rössler attractor | Smale's problems | strange attractor