There are many possible orbital shapes that a
planet can make in a binary star system. It depends on the masses of the two
stars, their separation, the mass of the planet, its distance from each star
and whether it is orbiting one star in the pair or both. At sufficient distances
the planet will revolve around both stars in an elliptical orbit. Closer in, the
orbit may be squashed into various shapes that slowly change orientation, much
like the patterns you get from a Spirograph. There are even orbits that trace
out long sausage shapes or the petals of a flower, or cross periodically between
the two stars. Complex orbits such as these may be rare, since many of them are
inherently unstable and would soon break down. Figure-of-eight orbits are not
possible.