n-body-fractal?

[Timeroot]

I just finished The Beauty of Fractals, and I learned that actually a Mandelbrot Set doesn't have to be related to constant addition. In fact, the "first" Mandelbrot Set was of the form z=c*(1+z^2)^2/(z*(z^2-1)), not z=z^2+c. The Julia Set, of course, is the "chaotic boundary", the points which never go to any attractor - infinite, fixed, periodic, or strange - but the Mandelbrot Set (for a given Julia Set) is just a control space for some parameter - any at all. For a polynomial map, that could mean z^c + 0.25. So with the N-body problem, I suppose the Julia Set would be a map of different initial positions and velocities for the stars. That's 8 dimensional, though, so you'd probably have to keep six as constants. You might get something where (for example) you have the location and velocity of one set, and the location of the other, and each point in the plane corresponds to a different velocity. Or maybe you have the locations of both set, and their angles of trajectory, and each point corresponds to a different initial speed.

Because these are the only parameters which affect the simulation (besides the timestep), that means - if you have a simple, Newtonian gravity - each point in the plane would have to correspond to a different mass. I suppose you could say that one star is the variable z, and the initial conditions of the other are a constant parameter which are used to calculate the changes on z...but who says we strictly need to stick the Msets and Jsets anyway, huh? We'll call it a Julibrot and do whatever we want with it