Hilbert Curve

A Hilbert Curve is a continuous fractal space-filling curve that maps a one-dimensional line onto a two-dimensional space, such as an area or grid. It is constructed through an iterative process, gradually increasing in complexity, creating a path that covers every point within a square without crossing itself. This property makes it useful for efficiently organizing data, image processing, and spatial indexing, as it preserves locality—points close in the curve are also close in space. The Hilbert Curve exemplifies how simple recursive rules can generate intricate patterns that fill space in a structured manner.