The Beauty of Space-Filling Curves: Understanding the Hilbert Curve

Space-filling curves (SFCs) are mathematical constructs that traverse every point in a continuous space, with practical applications in data science and engineering. The text traces their history from Georg Cantor's work on cardinality to the development of the Peano curve. It then focuses on the more famous Hilbert curve, detailing its recursive construction and key properties such as continuity, surjectivity, and locality preservation. This locality-preserving property is crucial for its use in modern data platforms like Databricks for optimizing data layout and processing. The article also introduces Skilling's algorithm as an effective method for computing the coordinates of points along the Hilbert curve.