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I am working on building a civilization that has a ingrained superstition about two body systems. My desire is to build a myth system that revolves around empty or 0 is bad, 1 is ideal, and 2 is troublesome, taken from the astronomical observations. I can do it using a lunar system, two moons where the primary moon has a visible secondary body at one of it's Lagrange points. If I understand what I have been reading about here this should be stable.
However, I want to take it one step further, and create a dual star system setup, using The Butterfly Pattern as the orbital system pattern. Do the dual stars make sense, and would the presence of two moons aggravate the system enough to be catastrophic in an approximate span of 500,000 - 1,000,000 cycles? (I am looking at this time span to be a possible evolutionary progression of the civilization) The population in question will be interstellar, and have deep religious trappings based on the cultural myths and superstitious paradigms.
(Edit:) This question started based on research into stable 3-body patterns from links in the figure-8 questions. However, the question is NOT whether a figure 8 works, but if there are physical models of orbits around two stars that give me all combinations of the stars in the perceived sky of the civilization's planet. Both answers have helped me and gave me a good place to keep working out the idea. I want to select both as an answer, since they both work off each other.