← Back to Labs
Hilbert Curve Fractal
Space-filling curve — every point in the square is visited exactly once
Order 1 — 4 points — length 3
The Hilbert curve (Hilbert, 1891) is a space-filling curve: its limit visits every point in the unit square. Order n divides the square into 4ⁿ cells; the path has length 4ⁿ−1 segments. Locality: nearby positions on the curve are nearby in space — making it invaluable for cache-coherent memory layouts, geographic indexing (R-tree / S2), and GPU texture mapping. Fractal dimension = 2.