The four three-body braids adopted in this study: the classic Figure-8 problem (top) and three more complicated braids, the unequal-mass problem, I.A.₄^i.c.(0.5), and $I.A{.}_{68}^{i.c.}(0.5)$ (bottom). They are integrated with a time-step parameter of η = 0.01 with output every 0.001 time units for one periodic orbit. The $I.A{.}_{68}^{i.c.}(0.5)$ braid is a complex orbit for which the period exceeds 83 time units, much more than any of the others. The orbit closes only after many orbits, giving rise to the filled-in surfaces. For the Figure-8, only one line color is visible because all three objects have the same orbit and therefore overlap.