A Peano-based space-filling surface of fractal dimension three

William Paulsen

Chaos, Solitons & Fractals, 2023, vol. 168, issue C

Abstract: Although space-filling curves are well known, and have many applications in parallel computing and data mapping, there is a need for a space-filling surface that is a continuous mapping from two-dimensional domain onto the unit cube. This would allow efficient implementation of a 2D problem on parallel processors which are interconnected into a 3D grid. Such a surface is presented in this paper, which uses Hilbert’s geometric approach to generate a mapping from a unit square to a triangular prism. Using two such mappings we can create a mapping from a rectangle to a unit cube. To culminate, we use the mapping to produce a continuous omnichromatic picture, that is, one for which the colors change continuously, and under sufficient resolution, contains every possible RGB value.

Keywords: Fractals; Hilbert curve; Peano curve; Space filling curves; Space filling surfaces; Omnichromatic picture (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000310

DOI: 10.1016/j.chaos.2023.113130

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