Update at the conclusion of my jam time.
I added some command line options so that a user can choose what system they'd like to visualize and the parameters for it. So far I have 4 built in systems.
I also extended the system to support 2nd order equations. 1st order equations are equations where you directly specify the velocity. These make the nice uniform flow fields. 2nd order equations are equations where you directly specify the acceleration. In that sort of system the position of a point doesn't uniquely determine it's velocity, so the plot becomes more of a cluster of particles shooting around one another. You can still see things like, what states the system tends to be drawn towards, whether the system tends to form orbitals or shoot off to infinity, etc.
I haven't gotten the code in a state where I can share it all yet, but you can check out the plotter here for now: https://mr-4th.itch.io/delta-xy-plotter
