Math Art

Dynamical systems can exhibit geometrically rich behavior, due in part to the uniqueness of solutions to ODEs. Under certain conditions, some systems remain confined to a finite subset of Euclidean space. Since the trajectories extend infinitely in time, they form infinitely long parametric curves in 3D space that remain within this bounded region. Because the trajectories are unique, they can never intersect at any point in time. As a result, each curve must weave around every other possible trajectory infinitely, yet still remain within the confined space. This behavior gives rise to the videos and some of the images of the systems shown below. The videos below were rendered offline with my 3D phase space simulation. The online version does not include a screen recording feature but does support taking screenshots.