This animation shows how solutions that are initially close together end up being all over the place as time evolves.pic.twitter.com/0u7YkAPa2u
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This is the Lorenz attractor, the chaotic trajectory of a 3D point with coordinates x,y,z solving a system of differential equations called the Lorentz system. The Greek letters σ,ρ,β are parameters. To get his butterfly-shaped attractor, Lorenz used the values σ=10, ρ=28, β=8/3.pic.twitter.com/fUiDjErAGE
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That's a demonstration of it right there!
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Sensitive dependence on initial conditions = butterflyeffect as referred to in my
#phd#dissertation is mathematically depicted by the logistic map. Feigenbaum’s constant = fascinating#proof#complexity#chaos is ordered.#entropyThanks. Twitter will use this to make your timeline better. UndoUndo
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Yes, if U r in Texas n Ur wife is in Brasil. :p ( humor)
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The story of how Lorenz began thinking about this is equally fascinating. Related to a precision error in the initial conditions of the weather model he was experimenting with at the time. ftp://texmex.mit.edu/pub/emanuel/PAPERS/Lorenz_Edward.pdf
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My favorite twitter account. Only interesting facts. Thank you!
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Interesting to see that the paper dismisses causality right in the intro whereas it is what prevailed in pop culture.
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