Towards the Gosper Space Filling Curve Implementation

Space filling curves (SFCs) are widely utilized in many research areas like point clustering, classification and machine learning, computer graphics, information visualization and/or image analysis. Mostly, the SFCs are based on the regular grids. Although a hexagonal grid has some outstanding properties, square and triangular grids are generally preferred. The construction of a hexagonal SFC is a complex task, because a hexagon cannot be decomposed into more uniform hexagons. This paper proposes an algorithm constructing a SFC imitating the Gosper curve. The Gosper curve is a self-similar fractal based on the hexagonal grid joining the hexagons to hexagon-like tiles. The novel Node-Gosper SFC is tested on 2D points clustering and compared with several SFCs. The results show that this method represents an interesting direction of points linearization and storing.