Quadtrees are everywhere spatial data exists. Mapping services use quadtree-like tile pyramids to serve map tiles at different zoom levels (Bing's quadkey system, for example, addresses tiles as base-4 paths). Game engines use them for collision detection and visibility culling. Geographic information systems use spatial indexes to store and query spatial datasets. PostGIS uses GiST indexes (R-tree-style) for spatial queries on geometries, while PostgreSQL's core supports quadtree-like SP-GiST indexes for certain data types like points.
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But that only goes so far. When someone in the crowd shouted "Play the Spice Girls!", he responded with a swift riposte: "Sorry, I don't take requests."