The Chinese Restaurant Process — customer n+1 joins table k with prob ∝ (people at k), or starts a NEW table with prob ∝ α
Restaurant empty — press Seat one or Auto-seat.
Each table is a cluster; the dish at a table is its shared parameter. Big tables pull harder (rich-get-richer); α sets the appetite for new tables. The number of tables is never fixed — the data grows it.