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August 25th, 2019, 11:39 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory  Chaotic, nonlinear, fractal
How do the properties chaotic, nonlinear and fractal interrelate?

August 26th, 2019, 09:06 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 
Nonlinear differential equations can have solutions such that a tiny change in initial conditions results in an enormous change in the solution trajectory. These solutions are known as chaotic as while they are entirely deterministic given the exact initial conditions, in practice this is never satisfied and the trajectories may as well be random. The boundary of sets of initial conditions that result in similar trajectories, at least in that they converge to the same attractor, can exhibit fractal geometry. That's the 30 second version. There are far more detailed and higher quality answers available on the web. 

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chaotic, fractal, nonlinear 
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