This YouTube video of a flip-dot display (physical b/w pixels) shows the reverse of an effect that might be called dissolve or dispersion, i.e. a text emerges from noise by pixels moving in to form letters. Here's a short cropped clip showing just the "crystallization" (wouldn't that be an appropriate name?):
(source: BREAKFAST NY)
For a particle system, I can imagine that "dissolving" every pixel (of a character) randomly wouldn't be too hard. Reversing the effect as shown in the video could be done using a precalculated sequence or even just animated sprites for each letter. Or, each pixel in the noise gets chosen to gravitate towards a letter (seems more complicated, may require clustering).
Then I found an implementation and live demo:
Particles text effects
Uses particles with a seek behavior to make up a word. The word is loaded into memory so that each particle can figure out their own position they need to seek. Inspired by Daniel Shiffman's arrival explantion from The Nature of Code. (natureofcode.com)
The reference resolves to
I think the effect is very similar, so I think they used a particle system.
Q: Is there an approach that does not require particles (i.e. less memory-expensive)?
Just for comparison, here's an attempt at creating a "normal" animated noise dissolve (random dither), as suggested in a comment, but I think it's obvious that the pixels in the original do move and it's not just a binary blending effect:
It requires at least one random value for each pixel: on which frame of the animation to become active.
This is what trichoplax's solution looks like (pseudorandomly swapping 10,000 neighboring pixels in each of 100 frames, and then reversing it using the same pseudorandom number sequence, just reversed):