> The pattern across any single frame is entirely random noise.
This is untrue in at least one sense. The patterning within the animated letters cycles. It is generated either by evaluating a periodic function or by reading from a file using a periodic offset.
Can't it be continuous random noise added at the top and then moved down each frame.
Roughly you create another full size rect. On each frame add a random pixel on row 1 and shift everything down.
Make that rest a layer below the top one which has Hello cut out as transparent.
In any single frame the result is random noise.