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Lorenz Attractor in GeoGebra Full tutorial now available: #mathematics #lorenz #attractor #differential #equations #geogebra

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∞ 𝕁uan ℂarlos

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14,121 次观看 • 2 年前 •via X (Twitter)

科学技术教育#mathematics#lorenz#attractor#differential#equations#geogebra
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The Thomas attractor is a mathematical concept in dynamical systems theory representing a type of chaotic space phase that exhibits cyclic symmetry. It was named after René Thomas, the mathematician who introduced it in 1979. The system is strictly related to the Lorenz attractor another famous chaotic evolutionary space manifold. The 3D Thomas attractor is represented by the combination of three differential equations where the symmetry is invariant under rotations of 120° (or 2π/3 radians) around the x y z axis which are the space coordinates, plus μ (mu) that is a parameter controlling the behavior. The attractor is characterized by a chaotic tendency and it’s sensitive to initial conditions, meaning that as μ increases, the motion undergoes period-doubling bifurcations leading to chaos. A good visualization of this spacetime manifold is a twisted, spiral-shaped structure with 3-fold symmetry where each spiral arm is symmetric with respect to the central axis, like the one displayed below. The chaotic evolution of this attractor demonstrates the geometric beauty and complexity of unpredictable systems.
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