I want to simulate a set of particles on a toroidal surface (a donut)
this so far it looks like the asteroids game, where if something goes off of one side, it reappears on the other. the particle class has a translate method that takes care of moving the particle and if it goes off of the edge, moving to the other side. so far this works.

here is a simplified version of the particle class

class Particle{
 public float X,Y;

 public translate(float dx,float dy){
   X += dx;
   Y += dy;
   if (X < 0){
     X = width;
   } else if (X > width){
     X = 0;
   }
   if (Y < 0){
     Y = height;
   } else if (Y > height){
     Y = 0;
   }
 }
}

Now I want to make all the particles mutually repulsive. I use a double for loop inside draw and calculate the net displacement of each particle, then I displace them all with that translate function like this.

 float dx,dy,dis,rad,ax,ay;
 for(int i=0; i<numCells; i++){
  mimi[i].sx = 0;
  mimi[i].sy = 0;
  for(int j=0; j<numCells; j++){
    if (i!=j){
      dx = mimi[j].X - mimi[i].X;
      dy = mimi[j].Y - mimi[i].Y;
      dis = sqrt(sq(dx)+sq(dy));
      rad = atan(dy/dx);
      ax = (1/dis)*cos(rad);
      ay = (1/dis)*sin(rad);
      if (dx > 0) ax *= -1;
      mimi[i].sx += ax*repulsiveForce;
      mimi[i].sy += ay*repulsiveForce;
    }
  }
  mimi[i].trans(mdx+mimi[i].sx, mdy+mimi[i].sy);
  mimi[i].draw();
 }

Since a torus is a closed surface, they should reach an equilibrium (especially with damping to help) but instead they are pushed to the edges are constantly popping between sides. each pop sends a shock wave through the particles and they never stabilize very well and require way too much damping.

Is there some other way I should be calculating the net displacement of each particle, so that equilibrium is reached? I want it to seem like a perfect torus from the particles perspective, without any simulation artifacts.

in other words, How the hell does Graviroids work?