The geometry and dynamics of binary trees

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

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 7, 1464-1481

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.

Keywords: Binary tree; Autoregulation; Dynamics (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:7:p:1464-1481

DOI: 10.1016/j.matcom.2010.04.020

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