Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
The Weierstrass function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo&...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/3/143 |
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| Summary: | The Weierstrass function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></munderover></mstyle><mrow><msup><mi>a</mi><mi>n</mi></msup><mo form="prefix">cos</mo><mrow><mo>(</mo><mn>2</mn><mi>π</mi><msup><mi>b</mi><mi>n</mi></msup><mi>x</mi><mo>)</mo></mrow></mrow></mrow></semantics></math></inline-formula> is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is still ongoing. In this paper, we summarize past researchers’ investigations on fractal dimensions of the Weierstrass function graph. |
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| ISSN: | 2504-3110 |