https://doi.org/10.1140/epjs/s11734-025-01637-5
Regular Article
Multifractal analysis on the attractors of perturbed iterated function systems
Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China
a priyankamohan195@gmail.com, priyanka@gzu.edu.cn
Received:
17
February
2025
Accepted:
15
April
2025
Published online:
24
April
2025
This paper develops perturbed iterated function systems to generate attractors, namely the perturbed fractal interpolation functions, by perturbing the vertical scaling parameter. The calculus of perturbed fractal functions is studied, and under necessary conditions on the perturbation parameter, the integral of perturbed fractal interpolation results in a different perturbed fractal function interpolating a different data set. Construction of perturbed fractal splines with additional condition on perturbation parameter has generalized the classical fractal splines. Further, multifractal measure is utilized as a quantitative measure to explore the heterogeneous distribution of newly developed perturbed fractal functions.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
