A Peano-based space-filling surface of fractal dimension three
Document Type
Article
Publication Title
Chaos, Solitons & Fractals
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.
DOI
10.1016/j.chaos.2023.113130
Publication Date
3-1-2023
Recommended Citation
Paulsen, William, "A Peano-based space-filling surface of fractal dimension three" (2023). Faculty Publications. 5.
https://arch.astate.edu/scm-mathfac/5
