Hilbert Curves in Two Dimensions

  • Ernesto Estevez-Rams Faculty of Physics-IMRE, University of Havana, 10400 Havana, Cuba. http://orcid.org/0000-0002-9062-572X
  • Yosdan Martínez-Camejo Instituto de Física, Universidade Federal de Uberlândia, 38408-100, Uberlândia-MG, Brasil.
  • Daniel Estévez-Moya Facultad de Matemática, University of Havana, San Lazaro y L. CP 10400. La Habana. Cuba.
  • Danilo Gómez-Gómez Facultad de Matemática, University of Havana, San Lazaro y L. CP 10400. La Habana. Cuba.
  • Beatriz Aragón-Fernández Universidad de Ciencias Informáticas, Carretera a San Antonio, La Habana, Cuba.

Abstract

The complete set of Hilbert curves in two dimensions is presented, comprising up to forty curves: 12 homogeneous and 28 inhomogeneous. The analytical expressions for all the homogeneous curves are derived, which are easily extendable to all forty curves. A tag system, that allows the construction of all curves, is also described.

Published
Jul 6, 2017
How to Cite
ESTEVEZ-RAMS, Ernesto et al. Hilbert Curves in Two Dimensions. Revista Cubana de Física, [S.l.], v. 34, n. 1, p. 9-18, july 2017. ISSN 2224-7939. Available at: <http://revistacubanadefisica.org/index.php/rcf/article/view/RCF_34-1_9>. Date accessed: 24 july 2017.
Section
Original Articles