Understanding Fractality: A Polyhedral Approach to the Koch Curve and Its Complex Dimensions
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| Název: | Understanding Fractality: A Polyhedral Approach to the Koch Curve and Its Complex Dimensions |
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| Autoři: | David, Claire, Lapidus, Michel |
| Přispěvatelé: | David, Claire |
| Zdroj: | Asymptotic Analysis. 145:1447-1465 |
| Informace o vydavateli: | SAGE Publications, 2025. |
| Rok vydání: | 2025 |
| Témata: | fractal tube formula, prefractal approximations, box-counting (or Minkowski) dimension, effective local and global tube zeta function, effective local and global distance zeta function, [MATH] Mathematics [math], 28A80 Koch Curve, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], MSC Classification: 11M41, Complex Dimensions of an IFD, MSC Classification: 11M41 28A12 28A75 28A80 Koch Curve prefractal approximations iterated fractal drum (IFD) Complex Dimensions of an IFD box-counting (or Minkowski) dimension fractal tube formula effective local and global tube zeta function effective local and global distance zeta function, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], 28A75, 28A12, iterated fractal drum (IFD), [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph] |
| Popis: | We extend our results about the Weierstrass Curve to the Koch Curve and provide exact expressions of the volume of polyhedral neighborhoods for the sequence of prefractal graphs which converge to the Koch Curve. We also introduce the associated local and global polyhedral fractal zeta functions . The actual poles of the global polyhedral fractal zeta function, which are all simple, yield the set of exact Complex Dimensions of the Koch Curve, a result which had never been obtained before. |
| Druh dokumentu: | Article |
| Popis souboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1875-8576 0921-7134 |
| DOI: | 10.1177/09217134241308435 |
| Přístupová URL adresa: | https://hal.sorbonne-universite.fr/hal-04348346v5 https://hal.sorbonne-universite.fr/hal-04348346v6 |
| Rights: | URL: https://journals.sagepub.com/page/policies/text-and-data-mining-license |
| Přístupové číslo: | edsair.doi.dedup.....d18119fa1a24182479bac25cd42fde78 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We extend our results about the Weierstrass Curve to the Koch Curve and provide exact expressions of the volume of polyhedral neighborhoods for the sequence of prefractal graphs which converge to the Koch Curve. We also introduce the associated local and global polyhedral fractal zeta functions . The actual poles of the global polyhedral fractal zeta function, which are all simple, yield the set of exact Complex Dimensions of the Koch Curve, a result which had never been obtained before. |
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| ISSN: | 18758576 09217134 |
| DOI: | 10.1177/09217134241308435 |