Arithmetic-Analytic Representation of Peano Curve

Guangjun Yang, Xiaoling Yang and Ping Wang

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-7

Abstract:

In this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a unit square and that the coordinate functions satisfy a Hölder inequality with index , which implies that the curve is everywhere continuous and nowhere differentiable.

Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2019/6745202.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2019/6745202.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6745202

DOI: 10.1155/2019/6745202

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().