So I got this weird idea that I would write a Processing sketch that simulates a closed 2d system (perhaps a sheet of metal totally insulated from the outside world) where some regions start out hotter than others and by heat being conducted the whole system comes to equilibrium. So I wrote this code (every frame the code determines the average temperature of the system and prints it out).

1. final int windowSize = 500;
   int[][] heatarray = new int[windowSize][windowSize];
   int totalheat = 0;
   
   void setup() {
     size(windowSize, windowSize);
     frameRate(30);
     for (int iii=0; iii<=(windowSize-1); iii++) { //windowSize-2 makes it go 0-499
       for (int jjj=0; jjj<=(windowSize-1); jjj++) {
         heatarray[iii][jjj] = round((noise(iii/200,jjj/200)*200));
       }
     }
   }
   
   void draw() {
     totalheat = 0;
     for (int iii=0; iii<=(windowSize-1); iii++) {
       for (int jjj=0; jjj<=(windowSize-1); jjj++) {
         stroke(heatarray[iii][jjj],heatarray[iii][jjj],heatarray[iii][jjj]);
         totalheat = totalheat+heatarray[iii][jjj];
         point(iii,jjj);
         htransfer(iii,jjj);
       }
     }
     println(totalheat/250000);
   }
   
   void htransfer(int iii,int jjj) {
     if ((iii>0) && (iii<499)) {
       if ((jjj>0) && (jjj<499)) {
         haverage(iii,jjj,iii+1,jjj+1);
         haverage(iii,jjj,iii+1,jjj-1);
         haverage(iii,jjj,iii-1,jjj+1);
         haverage(iii,jjj,iii-1,jjj-1);
       }
     }
   }
   
   void haverage(int x1,int y1,int x2, int y2) {
     int average = (heatarray[x1][y1]+heatarray[x2][y2])/2;
     heatarray[x1][y1] = average;
     heatarray[x2][y2] = average;
   }

Soooo try running the program. You'll see that *gasp* the average temperature of the system decreases every frame! This shouldn't happen, because this is supposed to be a closed system so there's nowhere for the heat to go! But yet it decreases. Can anyone find the bug? Help!