English Original
The Butterfly Effect is a concept in chaos theory describing a sensitive dependence on initial conditions (SDIC) within a dynamical system. This means that tiny variations in the starting state of a system can lead to vastly different outcomes over time. A common interpretation is that a small change can trigger a large chain of events.
In 1961, meteorologist Edward Lorenz discovered this effect while running a weather simulation. When he restarted a calculation using rounded input data (0.506 instead of 0.506127), the result diverged completely from the original run. This highlighted how minute differences could amplify.
Lorenz later popularized the idea with the poetic analogy: "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" This illustrates how a seemingly insignificant event might influence a large-scale system.
In his 1993 book The Essence of Chaos, Lorenz defined the Butterfly Effect as: "The present determines the future, but the approximate present does not approximately determine the future." This sensitivity limits long-term predictability in complex systems.
Scholars sometimes categorize the Butterfly Effect into different types, focusing on:
1. Sensitive dependence on initial conditions (the core definition).
2. The potential for a small disturbance to create organized circulation at a distance (less empirically verified in real weather).
3. How small-scale features, through nonlinear interactions, limit forecast accuracy.
中文翻译
蝴蝶效应是混沌理论中的一个概念，描述了动力系统对初始条件的敏感依赖性。这意味着系统初始状态的微小变化，会随着时间的推移导致截然不同的结果。一种常见的解读是：一个小小的变动可能引发一系列巨大的连锁事件。
1961年，气象学家爱德华·罗伦兹在运行天气模拟时发现了这一效应。当他使用四舍五入后的输入数据（0.506 而非 0.506127）重新启动计算时，结果与原始运行完全偏离。这揭示了微小的差异如何被放大。
罗伦兹后来用一个诗意的比喻推广了这个想法：“一只蝴蝶在巴西轻拍翅膀，会在德克萨斯州引起龙卷风吗？”这说明了看似微不足道的事件如何可能影响一个大规模系统。
在其1993年的著作《混沌的本质》中，罗伦兹将蝴蝶效应定义为：“现在决定未来，但近似的现在并不能近似地决定未来。”这种敏感性限制了复杂系统的长期可预测性。
学者们有时将蝴蝶效应分为不同类型，主要关注：
1. 对初始条件的敏感依赖性（核心定义）。
2. 微小扰动在远处产生有组织环流的可能性（在实际天气中较少得到实证验证）。
3. 小尺度特征如何通过非线性相互作用限制预测精度。