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Fractalization of Chaos and Complexity: Proposition of a New Method in the Study of Complex Systems

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Chaos, Complexity and Leadership 2020

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

Abstract

Proposition of new methods for the study of complex systems and chaos is working on the frontiers of knowledge and hence it calls for philosophical contemplation besides well-set empirical researches. Complex system studies still suffer methodological paucity. Hence, the research goal is proposing a new generic methodology in the domain of chaotic and complex systems’ behavior study. The research in the theorization section discusses the epistemology of the proposed method (philosophic belief, logical justification and mathematical warrant) for pattern formation in chaos and complexity. Later, in the section on how to use the method in practice, the procedures of finding recursions and their fractalization are illustrated for organizational power. Our discussions deepen generic understanding of the connections between chaos/complexity and fractalization and thus the potential disciplines for the implementation of the introduced method could be a large spectrum embracing the humanities to the natural sciences.

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Notes

  1. 1.

    “Philosophical theory of knowledge based on the assertion that the mind perceives only mental images (representations) of material objects outside the mind, not the objects themselves” [12].

  2. 2.

    “A view that asserts that entities of a given kind are identical to, or are collections or combinations of, entities of another (often simpler or more basic) kind or that expressions denoting such entities are definable in terms of expressions denoting other entities” [11].

  3. 3.

    Besides Warrant which could be interchangeably used in place of Justification.

  4. 4.

    In Logic, the symbols: ∧ (logical conjunction) means ‘and’, ¬ (negation) means ‘not’, ⇒ (material implication) means ‘implies’, ⇔ (material equivalence) means ‘the same as’.

  5. 5.

    This phrase is coined by the authors and it indicates any endeavor on the side of the researchers for finding meaningful repetitive – i.e. recursive - sets of numbers within the available data.

  6. 6.

    The software Fractal Real Finder is available online. See www.researchgate.net/profile/Cristina_Serpa, for information on how to download it and for support materials.

  7. 7.

    The software Fractal Real Finder is available online. See www.researchgate.net/profile/Cristina_Serpa, for information on how to download it and for support materials.

  8. 8.

    There is a simple and easy tutorial about this test on page: https://www.real-statistics.com/non-parametric-tests/goodness-of-fit-tests/two-sample-kolmogorov-smirnov-test/.

  9. 9.

    The computation of such an equation may be done in the page https://www.wolframalpha.com/.

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Acknowledgements

Cristina Serpa acknowledges partial support from National Funding from FCT—Fundação para a Ciência e a Tecnologia, under the project: UIDB/04561/2020.

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Authors and Affiliations

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

    Cristina Serpa

  2. University of Sistan and Baluchestan, Zahedan, Iran

    Amir Forouharfar

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  1. Cristina Serpa
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  2. Amir Forouharfar
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Correspondence to Amir Forouharfar .

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Editors and Affiliations

  1. Faculty of Education, Hacettepe University, Ankara, Turkey

    Şefika Şule Erçetin

  2. Faculty of Economics and Administrative Sciences, Ankara Hacı Bayram Veli University, Ankara, Turkey

    Şuay Nilhan Açıkalın

  3. Faculty of Political Science, University of Sarajevo, Sarajevo, Bosnia and Herzegovina

    Emir Vajzović

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Serpa, C., Forouharfar, A. (2021). Fractalization of Chaos and Complexity: Proposition of a New Method in the Study of Complex Systems. In: Erçetin, Ş.Ş., Açıkalın, Ş.N., Vajzović, E. (eds) Chaos, Complexity and Leadership 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-74057-3_8

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