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Computational Language Related to Recursion, Incursion and Fractal

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Language and Recursion

Abstract

This paper deals with the mathematical presentation of some computational formulas for characterizing natural and artificial languages, as the Zipf–Mandelbrot scaling law; the Shannon–Weaver entropy; and the Rényi generalized fractal dimensions with applications to fractal, multifractal and correlation dimensions of time series of texts. Turing machine is related to formal language and recursion. By recursive process, fractal can be generated. It is shown that fractal can be generated by incursion, an inclusive or implicit recursion. The fundamental property of incursion deals with the definition of a path that means that the iterations are ordered, contrary to the recursion which deals with parallel iterations. The main property is that the incursive fractal is invertible.

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Author information

Authors and Affiliations

  1. HEC-ULg, Management School of the University of Liege, Liege, Belgium

    Daniel M. Dubois

  2. ASBL CHAOS, Centre for Hyperincursion and Anticipation in Ordered Systems, Institute of Mathematics B37, Grande Traverse 12, BE 4000, Liege, Belgium

    Daniel M. Dubois

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  1. Daniel M. Dubois
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Correspondence to Daniel M. Dubois .

Editor information

Editors and Affiliations

  1. Department of Cognitive Sciences, University of Mons, Mons, Belgium

    Francis Lowenthal

  2. Department of Cognitive Sciences, University of Mons, Mons, Belgium

    Laurent Lefebvre

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Dubois, D.M. (2014). Computational Language Related to Recursion, Incursion and Fractal. In: Lowenthal, F., Lefebvre, L. (eds) Language and Recursion. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9414-0_12

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