This is what 812 double pendulums with different initial conditions look like [source, by Jonathan Nafziger: http://bit.ly/2BYPwbc] [interactive version: https://buff.ly/37Jsat5]
obviously there is no mechanical coupling or they would all sync up.. so its kinda crazy how there still seems to be some correlation/large scale features
I don’t think there’s any coupling, just a visual grid. The close initial conditions just stay correlated for a while before diverging. And the low-energy ICs stay correlated longer since overall amplitudes are small.