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For both: a burst lives on after Birth Rate drops to 0, and is drawn (particles, blobs) where a constant 0 draws nothing. Its particles move and age, and are gone after their Longevity. Seeking matches a simulation from 0, and moving an earlier key with the same current rate and cache key isn't served from stale checkpoints. A constant rate gives exactly the constant-rate simulation's particles, with or without a host.