Butterfly Effect

The butterfly effect is a concept from chaos theory that describes how tiny changes in the initial conditions of a complex system can lead to dramatically different outcomes over time. It was popularized by mathematician and meteorologist Edward Lorenz in the 1960s–1970s. While running weather simulations, he discovered that rounding a single small number (e.g., from 0.506127 to 0.506) caused wildly different results later on. This led to his famous metaphor: the flap of a butterfly's wings in one part of the world could theoretically set off a chain of events resulting in a tornado weeks later in another part. In simple terms, it's the idea of sensitive dependence on initial conditions — small actions or differences can have massive, unpredictable ripple effects in nonlinear systems like weather, economies, or even personal lives. The term became widely known through popular culture (especially the 2004 film The Butterfly Effect starring Ashton Kutcher, which uses time travel to show how altering small past events creates drastically altered — and often worse — futures). In everyday use, people often invoke it to mean "one small thing can change everything."