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The geometry and dynamics of binary trees

Author

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  • David, T.
  • van Kempen, Thomas
  • Huang, Huaxiong
  • Wilson, Phillip

Abstract

The modeling of a fully populated 3D tree able to regulate dynamically remains a relatively unexplored field. A non-dimensional representation of “autoregulation” coupled with an asymmetric binary tree algorithm has been developed. The tree has a defined topology as well as a spatial representation in 3D. An analysis using a simple linearization shows the systems dynamics when perturbed away from equilibrium. Results, based on previously published work by Karch and Schreiner are presented for a variety of parameters which provide different shapes of the tree and indicate a possible mechanism for “growing” the tree in specified directions. In addition the tree, through the use of local tagging has the ability to vary its size locally via a coupled set of conservation and reverting differential equations.

Suggested Citation

  • David, T. & van Kempen, Thomas & Huang, Huaxiong & Wilson, Phillip, 2011. "The geometry and dynamics of binary trees," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1464-1481.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:7:p:1464-1481
    DOI: 10.1016/j.matcom.2010.04.020
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    Cited by:

    1. Olena Kostylenko & Helena Sofia Rodrigues & Delfim F. M. Torres, 2019. "The spread of a financial virus through Europe and beyond," Papers 1901.07241, arXiv.org.

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