The geometry and dynamics of binary trees

: 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 it’s size locally via a coupled set of conservation and reverting differential equations.

• Type: Journal
• Year: 2011
• Where: MCS
• Authors: T. David, Thomas van Kempen, Huaxiong Huang, Phillip Wilson
• Keywords: Asymmetric Binary Tree, MCS 2011, Pattern Recognition, Tree, Unexplored Field