Classic chaotic system discovered by Edward Lorenz in 1963
Start from two very close points and observe how trajectories diverge over time
The Lorenz attractor was discovered by American mathematician and meteorologist Edward Lorenz in 1963 while studying atmospheric convection. It is a three-dimensional continuous dynamical system that demonstrates the core characteristic of chaos theory: sensitive dependence on initial conditions.
σ (Sigma): Prandtl number, ratio of momentum diffusivity to thermal diffusivity
ρ (Rho): Rayleigh number, describing the strength of the system's driving force
β (Beta): Geometric factor, related to the physical dimensions of the system
A strange attractor is the limit set of a chaotic system in phase space. The Lorenz attractor has the following characteristics:
The "Butterfly Effect" is a famous concept proposed by Lorenz in 1972: A butterfly flapping its wings in Brazil might set off a tornado in Texas. This metaphor vividly illustrates the extreme sensitivity of chaotic systems to initial conditions.
In the Lorenz system, even if two starting points are only 0.001 apart, after sufficient time their trajectories will completely separate, exhibiting completely different behavior patterns. This makes long-term weather prediction impossible.
In 1963, Edward Lorenz, then working at the Massachusetts Institute of Technology (MIT), published a landmark paper titled "Deterministic Nonperiodic Flow." He accidentally discovered this system while using computers to simulate atmospheric convection.
Once, he wanted to rerun a simulation. To save time, he entered data from the middle of the simulation, keeping three decimal places instead of the original six. To his surprise, the results were completely different from the original simulation. This accidental discovery revealed the core principle of chaos theory: sensitive dependence on initial conditions.