a very rudimentary simulation of the three-body problem. i was curious how far we could get with just euler's method and a small time step, and it turns out we can get something pretty visually interesting!

i was also curious about what would happen if the polar coordinates of the bodies over time were translated into rgb values and animated; the results are below.

warning: some of the transitions from this orbit are pretty abrupt, so there may be flashing colors.

the starting positions for the graphics above are for periodic orbit F₁₀ from this paper: https://arxiv.org/abs/1805.07980

This is what F₁₀ looks like when solved with ODE solver dop853 (according to the paper):

as you can see, although the overall shape is similar/recognizeable, the error in the calculations above grow fairly noticeable after just 2 periods.