Noise grid stops moving after a while

It does keep going, but it doesn’t keep displaying. Your problem is that you have global variables – in particular, speed (fart) – that you keep incrementing, until the number is so large your sketch doesn’t work anymore.

Try bouncing that value around between -1 and 1, for example:

float gridcelleStr =8; 
float gridBredde;
float gridHoejde;
float faktor = 2;
float fart;
float fart_diff = 0.0000002;
float xPos; 
float yPos; 
float tal; 
float strFaktor = 30;

void setup() {
  size(1200, 1200, P3D);
  gridBredde = floor(120);
  gridHoejde = floor(120);
  fart = 0;
  rectMode(CENTER);
  imageMode(CENTER);
}
void draw() {
  background(255);
  if (fart>1) {
    fart_diff = -0.0000002;
  }
  if (fart<-1) {
    fart_diff = 0.0000002;
  }
  for (int y = 0; y < gridHoejde; y++) {
    for (int x = 0; x <gridBredde; x++) {
      pushMatrix();
      translate(100, 80);
      fart += fart_diff;
      tal = floor(noise(x/gridHoejde, y / gridBredde, fart) * faktor);
      xPos = x * gridcelleStr;
      yPos = y * gridcelleStr;
      noStroke();
      fill(random(0), random(0), random(150, 255));
      rect(xPos, yPos, tal * strFaktor, tal * strFaktor);
      popMatrix();
    }
  }
}