Casual Friday — Klemperer's Dream

From John Dubinski’s Galaxy Dynamics simulations comes this beautiful examination of symmetry and chaos in galaxy interactions:

Dubinski has this to say about the simulation himself:

Nature provides us with random acts of gravitational violence in the form of galaxy collisions. Graceful spiral forms, tails and bridges are sculpted by these interactions. But we know how gravity works and galaxies are structured, so we can take the sculptors tool from Natures hand and play with it in a supercomputer removing the random element.

Klemperer found that special symmetric arrangements of particles could follow predictable orbits. These exact N-body solutions seem to have no natural counterpart and even Klemperer stated that he really just studied them for fun! In the same spirit, I have put galaxies in similar unnatural symmetric configurations to explore their evolution. One amazing consequence of Newtons laws of motion is that any system with some symmetry built in should preserve that symmetry even if complex dynamical behaviour is occuring. For the sequence of simulations here, it seems that symmetry is preserved even when spiral patterns emerge after the galaxies interact strongly. But by the end of each sequence, the symmetry is lost. So is Newton wrong after all? No! These nonlinear dynamical systems are unstable and become chaotic. Tiny deviations introduced by computer imprecision are eventually amplified and lead the system away from symmetry. So these simulations are not just for fun after all. They are an interesting illustration of the emergence of chaos in nonlinear dynamical systems.

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