The generator is the stochastic core. It reads an image and grows an embroidery design by making many small random choices, but every one of those choices is drawn from a single seeded stream. That is the whole trick: randomness gives you variety, and the seed makes the variety reproducible. The output is a pure function of the pair (image, seed), so the same pair always resolves to the same stitch plan, down to the last needle drop.
The point of seeding is that reproducibility becomes an anchor rather than a hope. A generative process that cannot be replayed is one whose results you can neither trust nor recover: run it twice, get two things, lose the first. Here the seed is the fixed reference the run is measured against. Change the seed and you get a genuinely different, one-of-one design from the same picture. Keep the seed and you can recover any design the engine has ever produced.
Because the randomness is bounded this way, the surprise of a generative process and the determinism of a manufacturing file can live in the same artefact. The generator supplies the surprise; the seed supplies the recovery.