There are quite a few little tricks in there. For purposes of clarity I've stripped away as much as possible and in some ways made if less efficient. In the example below there is only a single 'point' made out of a position and a movement vector. It bounces within the boundaries of the PImage. This is all basic stuff, just like in the metaballs example.

The effect is basically created in three steps:
1. Take the squared distance from the point (line 23)
2. Invert the whole thing (line 24) => toggle with 'z'
3. Create cool colors (line 26) => toggle with 'x'

Only in the metaballs example the inverted distance for all points is summed up (instead of just one), therefore creating brighter spots in areas with multiple metaballs.

Adapted Code

1. PVector loc = new PVector(); // it has a location
   
2. PVector mov = new PVector(1, 1); // it moves
   
3. PImage pi;
4. boolean invertOn, colorOn;
5.  
6. void setup() {
7.   size(640, 360);
8.   pi = createImage(160, 90, RGB);
9. }
10.  
11. void draw() {
12.   loc.add(mov); // it moves
    
13.  
14.   if (loc.x < 0) { mov.x = 1; } // boundaries to keep it within the PImage
    
15.   if (loc.x > pi.width) { mov.x = -1; }
16.   if (loc.y < 0) { mov.y = 1; }
17.   if (loc.y > pi.height) { mov.y =-1; }
18.  
19.   pi.loadPixels();
20.   for (int y = 0; y < pi.height; y++) {
21.     for (int x = 0; x < pi.width; x++) {
22.       int index = x + y * pi.width;
23.       float distance = sq(dist(x, y, loc.x, loc.y)); // the distance squared from the point
    
24.       if (invertOn) { distance = 60000/distance; } // inverted
    
25.       color c = color(distance);
26.       if (colorOn) { c = color(0, distance+x, (x+distance+y)/2); } // color effects
    
27.       pi.pixels[index] = color(c);
28.     }
29.   }
30.   pi.updatePixels();
31.  
32.   image(pi, 0, 0, width, height); // display PImage full screen
    
33. }
34.  
35. void keyPressed() {
36.   if (key == 'z') { invertOn = !invertOn; }
37.   if (key == 'x') { colorOn = !colorOn; }
38. }