eyal

int num, gap;  // declare the variables as global variables
float cellsize_X, cellsize_Y, offsetX, offsetY; // declare the variables as global variables

void setup() {
  size (600, 600);
  // rectMode(CORNER); > not necessary, it's the default
  noStroke();
  randomSeed(hour() + minute() + second() + millis()); // that's an interesting way to create the random seed! :)

  num = 25;  // no need for int(25) here! also, all these variables need only to be set once, not over and over again (also that works too in this case)
  gap = 0; // idem

  cellsize_Y = ( height - (num +1) * gap ) / (float) num;
  cellsize_X = ( width - (num +1) * gap ) / (float) num;

  offsetX = cellsize_X/16.0;
  offset = cellsize_Y/16.0;
}

void draw() {
  background (255);

  for (int i=0; i<num; i++) {
    for (int j=0; j<num; j++) { // you had i<num here! That's why you didn't see any rectangles!
      fill (255, 57, 57, 180);  // do not need a value higher than 255 as a value here
      rect(gap * (i+1) + cellsize_X * i, gap * (j+1) + cellsize_Y * j, cellsize_X, cellsize_Y);
    }
  }
}