Towards the Gosper Space Filling Curve Implementation

Abstract

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.