Frequency clustering and disaggregation in idealized fractal tree

Abstract: The pattern of formation of resonant frequency clusters in idealized sympodial dichasium trees is revealed by numerical modeling and analysis. The larger cluster's cardinality correlates with that of a Small World Network, which share the same adjacency matrix. Topology and inherent symmetry of the structure dictate compartmentalization of the modal characteristics and robustness to perturbations to the limb geometry, and are not limited to a specific allometry. When the spatial symmetry of the limb geometry is perturbed above a certain level, we see percolation of the largest cluster.