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Fractal Functions and the Dragon’s Mountain: A Functional Equations Perspective

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Chaos and Complex Systems

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

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Abstract

We use an iterative method to construct solutions of iterated functions systems. This suggests a characterization of fractal functions via an admissibility alphabet. In this context, we define a new fractal object called dragon’s mountain, a real valued function with a complex domain designated by dragon’s set. The fractal structure is induced on solution sets by this type of structure, using the tools of symbolic dynamics.

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Acknowledgements

The author acknowledges partial support by National Funding from FCT—Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2019.

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Authors and Affiliations

  1. Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Instituto Superior de Engenharia de Lisboa, Lisbon, Portugal

    Cristina Serpa

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  1. Cristina Serpa
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Correspondence to Cristina Serpa .

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Editors and Affiliations

  1. School of Science and Technology, International Hellenic University, Thessaloniki, Greece

    Stavros G. Stavrinides

  2. Department of Physics, Istanbul Kultur University, Istanbul, Turkey

    Mehmet Ozer

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Serpa, C. (2020). Fractal Functions and the Dragon’s Mountain: A Functional Equations Perspective. In: Stavrinides, S., Ozer, M. (eds) Chaos and Complex Systems. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-35441-1_4

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