Note: Wave equation's "phase" was off for this video for no particular reason. I will try to simulate a difraction pattern using it and upload the video some near day.
Well, it was not that way that the idea started... it was really the opposite: I was trying different ways to maximize a function with fractals, then I got sometinhg that resembled a lot to QED -to me- once I was able to undress it from all the "macro" misconceptions I was using.
Finally, QED simulation made a decent function "solver" (maximizing or minimizing) but this is another history. The reason I am talking about QED is just to show you a simple video of how this extrange thing behaves.
In the video, an electron and a particle similar to a proton (sorry, real protons still in beta) are trapped in a 2D electromagnetic trap (function being minimized is x²+y²+z²), so they attract each other, but at the same time they can not be in the same spot, so a repulsion appears at small distances (I didn't place it there, I swear!) that make them to stay a little apart.
A cloud of "virtual photons" dance around the particles in the video, forming nice spirals and reinforcing one to another into a stable configuration where both spirals rotate in opposite directions, in a nice and strange dance.
If you know about QED more than I do -not difficult at all- surely you will laught a little about the simplicity of my approach. Please do comment about it, I am willing to be ashamed for my deep ignorance ;-)
This example runs on a 2D euclidean space, but other options allow me to simulate it over a 3D space or even a Minkowsky 4D, where time is just another dimension. The resulting shapes are not so different to those in this video, but it sounds terrible nice to use a "Minkowsky space", doesn't it?
Tech note: This video is not "real time" recorded form my computers, but it could be so, the simulation is lighting fast and can be paralelized if I weren't so lazy!