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Growing a Self-Similar Tree

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Applications of Fibonacci Numbers

Abstract

In the Steinhaus’s popular book [7], he writes “If a tree puts forth a new branch after one year, and always rests for a year, producing a new branch only in the following year, and if the same law applies to each branch, then in the first year we should have only the trunk, in the second, two branches, in the third, three, then 5,8,13, etc., as in Fibonacci’s sequence.”

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References

  1. Gudder, S. A Mathematical Journey. 2nd Edition. N.Y.: McGraw-Hill, 1994.

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  2. Horibe, Y. “An Entropy View of Fibonacci Trees.” The Fibonacci Quarterly, Vol. 20 (1982): pp. 168–178.

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  3. Horibe, Y. “A Fibonacci Theme on Balanced Binary Trees.” The Fibonacci Quarterly, Vol. 30 (1992): pp. 244–250.

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  4. Horibe, Y. “On Dichotomous Complexity of the Fibonacci Tree.” Applications of Fibonacci Numbers. Volume 6. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996: pp. 251–256.

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  5. Jean, R.V. Phvllotaxis: a systemic study in plant morphogenesis. Cambridge University Press, 1994.

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  6. Sharp, W.E. “Fibonacci Drainage Patterns.” The Fibonacci Quarterly, Vol. 10 (1972): pp. 643–650, 655.

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  7. Steinhaus, H. Mathematical Snapshots. Oxford University Press, 1969 (First Edition: 1938).

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  8. Stevens, P.S. Patterns in Nature. Boston: tlantic Monthly Press/Little, Brown and Company, 1974.

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  9. Thompson, D’Arcy W. On Growth and Form, abridged edition. Cambridge University Press, 1961.

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Authors
  1. Yasuichi Horibe
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Editor information

Editors and Affiliations

  1. South Dakota State University, Brookings, South Dakota, USA

    G. E. Bergum

  2. House of Representatives, Nicosia, Cyprus

    A. N. Philippou

  3. University of New England, Armidale, New South Wales, Australia

    A. F. Horadam

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© 1998 Springer Science+Business Media Dordrecht

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Horibe, Y. (1998). Growing a Self-Similar Tree. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5020-0_21

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  • DOI: https://doi.org/10.1007/978-94-011-5020-0_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6107-0

  • Online ISBN: 978-94-011-5020-0

  • eBook Packages: Springer Book Archive

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