The complete set of homogeneous Hilbert curves in two dimensions

TL;DR

This paper catalogs all homogeneous Hilbert curves in two dimensions, introduces six new variants via reversion operations, and details their generation processes and representations.

Contribution

It provides the complete set of 2D homogeneous Hilbert curves, including six new ones, with detailed construction algorithms and tagging methods.

Findings

Six new Hilbert curves introduced.

Complete inventory of 2D homogeneous Hilbert curves.

Detailed affine transformation and tag system descriptions.

Abstract

An inventory of all possible homogenous Hilbert curves in two dimensions are reported. Six new Hilbert curves are described by introducing the reversion operation in the construction algorithm. For each curve, the set of affine transformation defining the generation process is reported. Finally, each curve is also described in terms of a tag system.