A proposal of hierarchical vertex clustering based on the Gosper curve

Space-filling curves (SFCs) are straightforward and efficient methods for a sparse space clustering. They are utilized in research areas like classification, computer vision, computer graphics and/or machine learning. Most of the SFCs are based on a regular orthogonal grid. Generally, a hierarchical properties of Quad-trees (2D) or Octrees (n-dimensional) are utilized for a vertex hashing. However, the regular hexagonal grid is applicable for 2D tiling as well. The hexagonal shape is principally not a reptile, so the construction of hexagonal SFCs or a query structure is still a complex task. The Gosper curve (Flowsnake) is a self similar fractal that groups the hexagons to a composite called the Gosper island. This paper proposes a novel method constructing a Gosper-like space-filling curve of 2D vertices. The final algorithm is tested on several datasets and the results are discussed.