There appears to be a problem where pixels write to the same buffer that later pixels read from. The example shows two pixels below the center; if you try to put them above the center the result image will grow much more slowly.
You are right, at each iteration, the information propagates all the way to the bottom, but climbs 1px at the time.
One interesting aspect is that if you draw something and iterate a few times, you will see the same drawing appear again.