Arithmetic-Analytic Representation of Peano Curve

Guangjun Yang, Xiaoling Yang, Ping Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 α=1/2, which implies that the curve is everywhere continuous and nowhere differentiable.

Original languageEnglish (US)
Article number6745202
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2019
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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