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- W2973210007 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:math>, which implies that the curve is everywhere continuous and nowhere differentiable." @default.
- W2973210007 created "2019-09-19" @default.
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- W2973210007 date "2019-09-10" @default.
- W2973210007 modified "2023-09-27" @default.
- W2973210007 title "Arithmetic-Analytic Representation of Peano Curve" @default.
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- W2973210007 doi "https://doi.org/10.1155/2019/6745202" @default.
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