The Lorenz attractor
“Predictability: can the beating of butterfly’s wings in Brazil cause a tornado in Texas?”
In 1963, Edward Lorenz (1917–2008), who was very interested by the problem of convection in the Earth’s atmosphere, drastically simplified the NavierStokes equations of fluid mechanics, well-known for their intricate complexity.
The Lorenz attractor
The Lorenz’ atmospheric model is what physicists use to call a toy model: although it is so oversimplified that it does not have much to do with reality anymore, Lorenz soon realized that this model was very interesting. If we consider two almost identical atmospheres (two points that are extremely close in Lorenz’ model), we tend to quickly see the separation of the two evolutions in a significative way: the two atmospheres become completely different. Lorenz saw on his model the sensitive dependence on initial conditions: chaos. Moreover, what is very interesting is that, starting from a large number of virtual atmospheres, even if they follow paths that seem a little bit crazy and unpredictable, they all accumulate on the same object shaped like a butterfly, a strange attractor.