Python to produce n-body simulations in 3D using matplotlib
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N Body Simulator

If you're looking for a good example of how to make animations using matplotlib's 3D scatterplots...

If you wanna see a real basic Newtonian time-stepped n-body model in action...

If you've forgotten what the Earth and Venus's orbit around the sun looks like...

Look no further.

Our Solar System

python home3 Works. Pretty phresh. See it on YouTube

Alpha Centauri

Many, many brownie points to anyone who can figure out why the Alpha Centauri simulation doesn't work. My only guess at the moment is that it's because conservation of energy isn't respected, but I'm skeptical since the orbit doesn't seem to get any better when the timestep is reduced.

A Note on Timestep Simulations

As mentioned above, in this simulation, energy and momentum are not conserved. You may notice that this is not how physics works. This is because e.g. energy is a smooth curve with particular points of symmetry about which certain pairs of integrals are equal in real life, while the same pairs of integrals on the time-stepped function, which looks like any other step function, are unlikely to be.