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 its size locally via a coupled set of conservation and reverting differential equations.