Hilbert Curve Generator

The Hilbert curve is a continuous space-filling curve that visits every point in a square grid. It was first described by the German mathematician David Hilbert in 1891 as a variant of the space-filling curves discovered by Giuseppe Peano in 1890.

Properties

• Hausdorff dimension: 2 -- the curve fills the entire 2D plane as the order approaches infinity.
• Continuity: The curve is continuous and passes through every cell in a 2ⁿ x 2ⁿ grid exactly once.
• Locality preservation: Points that are close together along the curve tend to be close together in 2D space, making it useful for spatial indexing.

Applications

• Database indexing: Used in spatial databases (R-trees, B-trees with Hilbert ordering) for efficient multidimensional queries.
• Image processing: Dithering, texture mapping, and scan ordering for cache-friendly memory access.
• Dimensionality reduction: Mapping multidimensional data to one dimension while preserving locality.
• Computer graphics: Efficient traversal of image pixels for rendering and compression.

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