Arithmetic-Analytic Representation of Peano Curve

Guangjun Yang; Xiaoling Yang; Ping Wang

doi:10.1155/2019/6745202

Arithmetic-Analytic Representation of Peano Curve

Guangjun Yang, Xiaoling Yang, Ping Wang

Penn State Schuylkill

Research output: Contribution to journal › Article › peer-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 language	English (US)
Article number	6745202
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2019
DOIs	https://doi.org/10.1155/2019/6745202
State	Published - 2019

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1155/2019/6745202

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title = "Arithmetic-Analytic Representation of Peano Curve",

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 H{\"o}lder inequality with index α=1/2, which implies that the curve is everywhere continuous and nowhere differentiable.",

author = "Guangjun Yang and Xiaoling Yang and Ping Wang",

note = "Publisher Copyright: {\textcopyright} 2019 Guangjun Yang et al.",

year = "2019",

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AB - 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.

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DO - 10.1155/2019/6745202

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JO - International Journal of Mathematics and Mathematical Sciences

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Arithmetic-Analytic Representation of Peano Curve

Abstract

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