In physicsmata 1.2.1 (that exact version demonstrates it best, not 1.2.2 which is more about something else)

http://sourceforge.net/projects/physicsmataI created a cube full of 400 random points, and for each chose some near points, observed their exact distance, and put a distance constraint between those pairs. Each time cycle, every point moves the same constant distance in whatever direction its constraints are most satisfied, as if they were springs of constant length, except instead of spring force its not acceleration or force as we know it, instead its a change of position. I have no speed variable, just these vibrating jumps of C (or call it 1.0) distance each. Its C instead of C^2 because if you sum C^2 coin flips each as -1 or 1, its on a bell curve of standard deviation exactly C, as you can see in pascals triangle which is not normally used for that but its where bell curves and circles come from.

When you drag with the mouse the cube of points with distance constraints, angular momentum is conserved as you see by the other half of it rotating the opposite direction you're pulling some point. Drag it along the side of the window and see twisting, bending, and vibrating of that jello-like cube space.

But the electric induction needs an extra step... Instead of manually choosing the distance constraints, which are spread around a sphere with varying radius (so it is compatible with the following math), it would be the inverse distance squared (as in newtonian gravity, electric/magnetic fields, etc), probably with a slight adjustment for the delay in the points at a distance reaching here, but you've got to use a finite set of points somewhere in a simulation.

Whats the 4-vector of it? Light speed appears constant to everyone, happens for the same reason alternating current (AC) squashes together the top humps in the wave and pulls apart the bottom humps (or however you want to name it, since it is symmetric as the phase covers everywhere once per wavelength), so when the 2 sides of a top hump are approaching eachother they are going this constant C 1.0 speed toward eachother, then reversing, back and forth in some combination, whichever way is epsilon less than 0 or epsilon more than 0 (discontinuous, quantum, pascals triangle, converges to bell curve as these forward/back zigzags are like coin flips). The squashing toward the tops see eachother through the denser space, and those farther apart see eachother through the less dense space. This happens when the electric company pushes and pulls on our power lines 60 times per second.

In an induction coil, for example, the many coils near eachother going in the same direction would do the same thing to eachother, cause eachother to jump forward/back/zigzagging 1.0 C that constant distance in some direction. The curl of magnetic field, as perpendicular to the electric field, is lorentzed from choosing a unit vector (from a sphere center to its surface), or maybe its a 3-sphere (as in poincare) with 1 more dimension we call spin or phase or something. Lorentz is just the equation of a circle. Any time you do a sine or cosine, thats the basic idea of lorentz.

There is no total field in a sphere shell. No gravity. No electric. So what does that mean when ball lightning forms a sphere shell, turns invisible, goes through solid objects without much touching them, and eventually explodes with a every loud noise and produces a burned sulfur smell (I read)? I'd say the electricity is moving in these constant distance jumps, back and forth, as it runs into a big blob of lightning and turns sideways starting to cover a sphere, and since its already the amount of positive/negative that lightning would exist there (because a positive charge pulls the negative lightning), I'm not sure if there is a positive charge in its center or not, especially because of that youtube video showing how to turn a sphere insideout without pinching a surface since that means a sphere has only 1 side.

I'm going to try simulating ball lightning, coil inductor, capacitor, etc... Something simple like a blob of bell curves I'll call wire and metal plates, and coil the wire in the middle, and for the lightning that would take a slower but very worth it to see what happens simulation. Science is also good for games. The jello-like cube of 400 points runs realtime graphics fast without even much optimizations. This is because I found the right math instead of needing to evolve possible solutions to the constraints. You just calculate it right away each time cycle. Try it.