Dynamic systems
Text written by Bojan Crnković, Faculty of Mathematics, University of Rijeka
In 1963, Edward Lorenz, Ellen Fetter and later Margaret Hamilton were responsible for the numerical simulations, images and numerical calculations that led to the discovery of the Lorenz model. The Lorenz model is a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as Lorenz’s equations.
Apart from the obvious similarity of the Lorenz model visualization to a butterfly, the connection is often illustrated by the concept of the “butterfly effect”. A Lorenz attractor is a mathematical model that describes a chaotic system that exhibits a sensitive dependence on initial conditions. This means that small changes in the initial conditions of the system can lead to very different results over time.
The term “butterfly effect” was coined by mathematician and meteorologist Edward Lorenz, who discovered this phenomenon while studying the weather. He famously noted that the flapping of a butterfly’s wings in Brazil can set off a series of events that lead to tornadoes in Texas. This shows how small changes in one part of the world can have significant consequences elsewhere.
The connection between the Lorenz attractor and the butterfly is therefore a metaphor that illustrates how seemingly insignificant actions or events can have far-reaching and unpredictable effects.