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The Lorenz system is a model that describes chaotic behavior in atmospheric convection. Its study reveals how small changes in initial conditions can lead to different outcomes.

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Samuel Vaiter

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11,386 görüntüleme • 1 yıl önce •via X (Twitter)

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We just wrote a single pdiffeq for a set of periodic vector functions and a pair of geometric minimum solutions from which all other diffeqs (e.g. turbulence) in the universe are derived. Quantum gravity came along for the ride. Simplified intro video:

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The Lorenz system is a classic example of the “butterfly effect,” where small changes in initial conditions lead to very different outcomes. In this visualization, we simulated the Lorenz attractor using MATLAB and Claude with 10 slightly varied starting points.
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The Lorenz system is a classic example of the “butterfly effect,” where small changes in initial conditions lead to very different outcomes. In this visualization, we simulated the Lorenz attractor using MATLAB and Claude with 10 slightly varied starting points.

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A tiny change can change everything. The Lorenz system demonstrates the “butterfly effect,” where subtle differences in initial conditions lead to very different outcomes. This simulation visualizes that divergence across 10 starting points. Check it out ⤵️ 🦋
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There truly is an underlying order in every chaotic system In this scene, we have 2500 identical triple pendulums on a grid with almost the same initial conditions.
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Predicting a double pendulum is physically impossible in the long term because it is a deterministic chaotic system. While the exact equations of motion are known, infinitesimal differences in initial conditions—such as a millionth of a degree—will cause the trajectories to diverge completely almost immediately. © Science Facts
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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission
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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission
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