Skip to main content
SpringerLink
Log in
Book cover

Handbook of the Mathematics of the Arts and Sciences pp 1–18Cite as

Designing Binary Trees

  • Living reference work entry
  • First Online:

  • 197 Accesses

Abstract

Binary trees are usually defined so that left and right branches are determined by scaled rotations. However, when arbitrary affine transformations are allowed, a wide variety of trees may be produced. By varying parameters in the transformations, it is possible to produce trees with interesting geometrical properties. This paper explores the inverse problem: if it desired that a tree is to possess a specific geometrical property, find out which pairs of left/right branching transformations produce trees with this property.

This is a preview of subscription content, log in via an institution.

References

  • Espigulé B (2013) Generalized self-contacting symmetric fractal trees. Symmetry Cult Sci 21:333–351

    MATH  Google Scholar 

  • Mandelbrot B, Frame M (1999) The canopy and shortest path in a self-contacting fractal tree. Math Intell 21:18–27

    Article  MathSciNet  Google Scholar 

  • O’Hanlon A, Howard A, Brown D (2004) Path length and height in asymmetric binary branching trees. Missouri J Math Sci 16:88–103

    Article  Google Scholar 

  • Taylor TD (2007) Golden fractal trees. In: Sarhangi R, Barrallo J (eds) Bridges Donostia: mathematics, music, art, architecture, culture. Tarquin Publications, London, pp 181–188

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Independent Scholar, St. Petersburg, FL, USA

    Vincent J. Matsko

Authors
  1. Vincent J. Matsko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  2. Department of Mathematics Education, College of Education, Seoul National University, Seoul, South Korea

    Kyeong-Hwa Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Matsko, V.J. (2020). Designing Binary Trees. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_131-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70658-0_131-1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation