Space filling curves like Hilbert sound esoteric but they’re actually useful in for high performance database indexing.

DuckDB has a Hilbert index.

https://github.com/rustyconover/duckdb-lindel-extension

It’s not just DuckDB. SQL server and Postgres support Hilbert too.

The big idea is that you can project tuples e.g (lat, long) or just about any other tuple structure (string or floats) in a single integer, ordered in a way that is locality preserving.

Because most queries tend to lookup data close to each other, this can lead to performance gains. Parquet statistics can be built to be locality sensitive (locality defined broadly, not just numbers).

If you index on Hilbert, you can specific compute a max min of the Hilbert range of your predicate and eliminate looking outside that range, speeding up query performance.