2022/04/23 by Ozkaraca, Mustafa Ismail
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2204.11111
Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild condition. The generated space-filling curves for some known substitutions are elucidated. Some of those substitutions further induce relatively dense fractal-like sets in the plane, whenever some additional assumptions are met.