At the turn of the millennium, Carles Simó discovered several hundred planar three-body gravitational choreographies, and here they are in your browser:
Gravitational choreographies are periodic solutions of gravitational systems in which all bodies traverse the same orbit at equally spaced intervals. A system that starts off entirely in a plane, with no velocity components normal to the plane, will remain in the plane. For the choreographies presented here, the first third of the orbit is red, the second blue and the third green.
The data available on the linked website is formatted for presentation with the open-source application gnuplot. While one can certainly avail oneself of that resource, it is convenient to visualize the choreographies interactively without the need for downloading, compiling and running desktop software.