论文标题
Lebesgue类型填充曲线的平面替换和飞机上相对密集的分形套件
Planar Substitutions to Lebesgue type Space-Filling Curves and Relatively Dense Fractal-like Sets in the Plane
论文作者
论文摘要
Lebesgue曲线是一条填充空间曲线，通过线性插值填充了单元正方形。在这项研究中，我们概括了Lebesgue的构造，以产生填充空间曲线，从任何给定的平面替代，满足轻度条件。阐明了一些已知取代的生成的空间填充曲线。每当满足其他一些假设时，这些取代中的一些进一步诱导了平面中相对密集的分形样集。
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.
