3D Hilbert curve with 4 bits per axis traversing 4096 points (Image by author)
Space-filling curves (SFC) are fascinating mathematical constructs with many practical applications in data science and data engineering. While they may sound abstract, they’re often hiding in plain sight—behind terms like Z-ordering or Liquid Clustering (used, for example, in platforms like Databricks). If you’ve worked with large-scale data platforms, chances are you’ve already used SFCs without realizing it.
Despite its relevance in modern systems, information on this topic is often fragmented, making it difficult to bridge theory and practice. This article aims to bridge that gap, while focusing on the Hilbert curve.
