[GiF] Animating the Lorenz attractor with thousands of initial conditions

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MODERATOR NOTE: a submission to computations art contest, see more: Computational Art Contest 2022 - Staff Picks - WOLFRAM COMMUNITY
check the particle’s point of view version here: [GiF] Lorentz attractor animation: from the particle's point of view - Staff Picks - WOLFRAM COMMUNITY

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YouTube video: https://youtu.be/DI504zatHCI

Twitter post: Ben Bartlett on X: "It's called the Lorenz 𝘒𝘡𝘡𝘳𝘒𝘀𝘡𝘰𝘳 because all nearby points are 𝘒𝘡𝘡𝘳𝘒𝘀𝘡𝘦π˜₯ into the set of chaotic orbits, regardless of initial conditions" / X

Math animations collection: https://muon.people.stanford.edu/math-animations

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[GiF] Lorentz attractor animation: from the particle's point of view
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Nice animation, great colors. Joan Birman has an interesting paper on arxiv β€œLorenz Knots”, which inspired me to try and get a better understanding of attractor topology. The Lorenz equations are a multiway system whose structure is essentially that of the tent map, as can be deduced by analysis of the knot template given by Birman. Existence of periodic limit cycles in the Lorenz flow is then seen roughly equivalent to existence of periodic cycles in the tent map. Anyone who has worked through Predrag Cvitanović’s book on chaos knows what a difficulty it can be to find initial conditions, certainly not as easy as listing rational numbers. There seems to be much more to do in this field of chaotic oscillator analysis. Unfortunately, knot recognition is such a difficult problem, we can’t easily generate topological data, which we would need to move forward. Happy Plotting!

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Where can I find AnimationTools ?

The code makes a lot of .pngs, so I’m guessing there is function in the toolkit that will assemble them into a movie.

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