Fractal Interpolation Using Harmonic Functions on the Koch Curve
| Autor: | SongIl Ri, Song-Min Nam, Vasileios Drakopoulos |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Hölder continuity lcsh:Mathematics lcsh:QA299.6-433 Statistical and Nonlinear Physics lcsh:Analysis lcsh:Thermodynamics Koch Curve Koch snowflake lcsh:QA1-939 Fractal analysis interpolation Iterated function system Fractal fractal functions Harmonic function lcsh:QC310.15-319 Attractor Applied mathematics Differentiable function Analysis harmonic functions Interpolation Mathematics |
| Zdroj: | Fractal and Fractional Volume 5 Issue 2 Fractal and Fractional, Vol 5, Iss 28, p 28 (2021) |
| ISSN: | 2504-3110 |
| DOI: | 10.3390/fractalfract5020028 |
| Popis: | The Koch curve was first described by the Swedish mathematician Helge von Koch in 1904 as an example of a continuous but nowhere differentiable curve. Such functions are now characterised as fractal since their graphs are in general fractal sets. Furthermore, it can be obtained as the graph of an appropriately chosen iterated function system. On the other hand, a fractal interpolation function can be seen as a special case of an iterated function system thus maintaining all of its characteristics. Fractal interpolation functions are continuous functions that can be used to model continuous signals. An in-depth discussion on the theory of affine fractal interpolation functions generating the Koch Curve by using fractal analysis as well as its recent development including some of the research made by the authors is provided. We ensure that the graph of fractal interpolation functions on the Koch Curve are attractors of an iterated function system constructed by non-constant harmonic functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|