#PhysicsFactlet
The Lorenz system is a common example of chaotic dynamics and of a strange attractor.
Points with very similar initial conditions initially evolve very similarly to each other, until their trajectories diverge from each other, and start moving on a "butterfly"-shaped fractal. #Physics#Chaos
@j_bertolotti if you used approximations with a numerical method to draw these curves, aren't the approximation errors very much impacting the curves after some time because it's chaotic? I've often wondered about that
@j_bertolotti@bleuje But Etienne is correctly concerned that in chaotic dynamics, the error grows exponentially with time, so you would have to stop very quickly! A more relevant result is the shadowing lemma:
"Although a numerically computed chaotic trajectory diverges exponentially from the true trajectory with the same initial coordinates, there exists an errorless trajectory with a slightly different initial condition that stays near ("shadows") the numerically computed one. Therefore, the fractal structure of chaotic trajectories seen in computer maps is real."
Released into the #PublicDomain and uploaded to Wikimedia Commons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Lorenz_System_Lyapunov_time.webm
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