Pretty cool! @jamportz you should look into rendering the static separatrices along with the advected points/streamlines. It’s both fun to do and really increases the usefulness of the imagery to have some visual analysis. (This discussion might help with implementation details, if you’re interested: https://mathematica.stackexchange.com/questions/80284/plotti...)
Thanks for the suggestion, that does look like a nice way to visualize the structure of the phase space.
I'm not sure it's easy to implement this though, as it requires first solving for the equilibrium points of the flow, which in general requires solving a set of non-linear equations. That could maybe be attempted numerically, but it's likely to be difficult to make it fast/robust (not to mention, to implement it at all in WebGL shaders).
Also, in three dimensions are the separatrices still lines, or they can also be 2d surfaces? I'm not sure how they would be rendered if they can live on surfaces
It's definitely harder to implement than advection, yes. But IIRC it wasn't too bad at least for the Lorenz attractor. It has been a long time since I did my own Lorenz visualizer. Some systems certainly might be tougher. Pretty sure I did the separatrices numerically.
Separatrices can be surfaces in 3d systems. I suspect surfaces are less common than curves, but I'm just guessing. And maybe if you want it to be general, then how common is irrelevant anyway.
