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Multiple Fibonacci Trees

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Part of the Emergence, Complexity and Computation book series (ECC,volume 42)

Abstract

In this paper, we synthetise the studies of three papers we deposited on arXiv: see [7,8,9]. The paper considers the extension of the representation used in many of the author’s papers about cellular automata in the hyperbolic plane. In those papers, a particular representation of the natural numbers allows us together with the construction of a corresponding tree to define a coordinate system which can be used to navigate in the corresponding tiling of the hyperbolic plane. We extend those considerations to many other kinds of trees for the same purpose and we also extend the technique used for the tilings \(\{5,4\}\) and \(\{7,3\}\) to the tilings \(\{p,4\}\) and \(\{p+2,3\}\) of the same hyperbolic plane.

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  • DOI: 10.1007/978-3-030-92551-2_17
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  7. Margenstern M (2019) About Fibonacci trees - I -, 17pp. arXiv:1904.12135 [cs.DM]

  8. Margenstern M (2019) About Fibonacci trees - II - : generalized Fibonacci trees, 35pp. arXiv:1907.04677 [cs.DM.]

  9. Margenstern M (2019) About Fibonacci trees III: multiple Fibonacci trees, 35pp. arXiv:1909.01893 [cs.DM.]

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Margenstern, M. (2022). Multiple Fibonacci Trees. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-92551-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92550-5

  • Online ISBN: 978-3-030-92551-2

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