Evolving trajectories of the N-body problem

The N-body problem in k dimensions is the task of determining the time evolution of a system of kN second order ordinary differential equations according to Newtonpsilas inverse square law. It comes up in astrophysics as an approximation to celestial systems. Separately, evolved art is the use of evolutionary computation to create artistic works, visual or otherwise. This study attempts to use the trajectories of 4-rotationally symmetric 2-dimensional N-body initial conditions computed under leapfrog integration as visual art. The integration routine inevitably accumulates roundoff error; the initial conditions are evolved separately to both minimize and maximize the number of timesteps before the system becomes unstable. Unexpectedly, genes evolved to maximize the number of timesteps can reach thousands of times the number from random genes; evolving to minimize creates configurations declared unstable in the first timestep. Visual inspection of the pictures obtained also reveals common motifs among high and low fitness genes: two co-circling planets for high fitness, circling close to the center and being far off for low fitness. Some genes do not follow the motifs and are considered visually appealing by the author. The fitness landscape under this representation is highly multimodal with lots of sharp peaks and troughs, and mostly flat outside.