The Lorentz attractor exemplifies sensitive dependence from "summary" of Chaos by James Gleick
The Lorentz attractor, that tangled, three-lobed figure shown on screens around the world, exemplifies sensitive dependence. This means that even the tiniest disturbances can lead to drastically different outcomes. The attractor's structure captures a fundamental property of chaotic systems: their sensitivity to initial conditions. The Lorentz attractor, with its intricate shape, demonstrates how a system can be deterministic yet unpredictable. Edward Lorenz, the meteorologist who stumbled upon chaos theory, discovered that small changes in initial conditions could lead to vastly different weather predictions. He found that a slight variation in input values could produce dramatically divergent results. This sensitivity to initial conditions is a hallmark of chaotic systems, where tiny differences cascade into significant deviations over time. The Lorentz attractor's intricate form reflects the complex behavior of chaotic systems. Its three lobes represent the system's sensitivity to initial conditions, showing how small perturbations ...
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