The quadtree is the two-dimensional case of a broader family of space-partitioning data structures. Octrees extend the same idea to three dimensions (splitting cubes into eight children), KD-trees use alternating axis-aligned splits (splitting along x, then y, then x again), and R-trees group nearby objects into bounding rectangles. Each variant makes different tradeoffs between construction time, query speed, and update cost.
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The curtain of reality had pulled back for me, and I could no longer pretend to be ignorant of these eldritch possibilities. I furiously began to map the known breakfasts. If the dark breakfast exists, I must be able to find it in the interstices of the normal familiar world.