Attainment of maximum cube-to-linear ratio for three-dimensional Peano curves

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• 作者：E. V. Shchepin
• 关键词：three ; dimensional Peano curve ; q ; adic Peano curve ; fractal Peano curve ; polyfractal Peano curve ; fractal genus ; cube ; to ; linear ratio ; square ; to ; linear ratio
• 刊名：Mathematical Notes
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：98
• 期：5-6
• 页码：971-976
• 全文大小：606 KB
• 参考文献：1.M. Bader, Space-Filling Curves. An Introduction with Applications in Scientific Computing, in Texts Comput. Sci. Eng. (Springer-Verlag, Berlin, 2013), Vol. 9.
  2.E. V. Shchepin, “On fractal Peano curves,” in Trudy Mat. Inst. Steklov, Vol. 247: Geometric Topology and Set Theory (2004), pp. 294–303 [Proc. Steklov Inst.Math. 242 (4), 272–280 (2004)].
  3.H. Haverkort, An Inventory of Three-Dimensional Hilbert Space-Filling Curves, arXiv: 1109.2323v1 (2011).
  4.D. K. Shalyga, “On exact calculation of the cube-to-linear ratio for Peano curves,” Preprint no. 88 IPM im. M. V. Keldysha RAN (Keldysh Inst. Appl.Math., Russian Academy of Sciences, 2014).
  5.E. V. Shchepin and K. E. Bauman, “Minimal Peano curve,” in TrudyMat. Inst. Steklov, Vol. 263: Geometry, Topology, and Mathematical Physics. I (2008), pp. 251–271 [Proc. Steklov Inst. Math. 263 (1), 236–256 (2008).
  6.E. V. Shchepin, “On Hölder maps of cubes,” Math. Notes 87 (5-6), 757–767 (2010).MATH CrossRef
  
• 作者单位：E. V. Shchepin (1)
  
  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

The class of so-called q-adic Peano curves is defined, which is large enough to include the polyfractal curves. The cube-to-linear ratio for this class attains its maximum value, which can be effectively determined by an exhaustive search implementable on modern computers. Keywords three-dimensional Peano curve q-adic Peano curve fractal Peano curve polyfractal Peano curve fractal genus cube-to-linear ratio square-to-linear ratio