On the morphisms of fractal curves that increase their smoothness

Authors

  • Kirill Kamalutdinov Novosibirsk State University, Novosibirsk 630090, Russia Corresponding Author

DOI:

https://doi.org/10.66147/lnaa.20231117

Keywords:

Self-affine set, fractal interpolation function, self-similar zipper, Jordan arc

Abstract

We propose a construction which transforms a self-similar zipper in \(\mathbb R^n\) to a self-affine zipper \(\mathbb R^{n+1}\) whose attractor is a smooth curve.

References

[1] V. V. Aseev, A. V. Tetenov, A. S. Kravchenko On Self-Similar Jordan Arcs in Plane, Siberian Mathematical Journal, 2003, Volume 44, Issue 3, 379-386 DOI: https://doi.org/10.1023/A:1023848327898

[2] V. V. Aseev, A.V. Tetenov, On the Self-Similar Jordan Arcs Admitting Structure Parametrization, Siberian Mathematical Journal, 2005, Volume 46, Issue 4, 581-592. DOI: https://doi.org/10.1007/s11202-005-0059-1

[3] M. F. Barnsley, Fractal functions and interpolation, Constructive Approximation, 1986, 2, 303-329. DOI: https://doi.org/10.1007/BF01893434

[4] J. Hutchinson, Fractals and self-similarity, Indiana University Mathematics Journal, 1981, 30, 713-747. DOI: https://doi.org/10.1512/iumj.1981.30.30055

[5] A. S. Kravchenko, Smooth self-affine zippers, Sobolev Math Institute, preprint, Novosibirsk, 2005. (Russian)

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Published

2023-02-19

Issue

1 (2023) No. 1

Section

Articles

License

Copyright (c) 2023 Kirill Kamalutdinov (Corresponding Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On the morphisms of fractal curves that increase their smoothness. (2023). Letters in Nonlinear Analysis and Its Applications, 1(1), 47-51. https://doi.org/10.66147/lnaa.20231117