An Exploration of the Emergence of Pattern and Form from Constraints on Growth

Holly Dale


Growing structures are subjects of the space in which they develop. When space is limited or growth is constrained complex patterns and formations can arise. One example of this is seen in the bark patterns of trees. The rigid outer bark layer constrains the growth of the inner layers, resulting in the formation of intricate fracture patterns. An understanding of bark pattern formation has been hampered by insufficient information regarding the biomechanical properties of bark and the corresponding difficulties in faithfully modeling bark fractures using continuum mechanics. Grasstrees, however, have a discrete bark-like structure, making them particularly well suited for computational studies. In this thesis I present a model of grasstree development capturing both primary and secondary growth. A biomechanical model based on a mass-spring network represents the surface of the trunk, permitting the emergence of fractures. This model reproduces key features of grasstree bark patterns which have the same statistical character as trees found in nature. The results support the general hypothesis that the observed bark patterns found in grasstrees may be explained in terms of mechanical fractures driven by secondary growth and that bark pattern formation is primarily a biomechanical phenomenon. Furthermore, I extend the grasstree model to analyze the patterning of discrete elements on the surface of pandanus fruit. Pandanus fruit also exhibit patterns apparently related to fracturing and constraints of space. In this case, the results show that the pattern is likely a result of a higher level mechanisms as opposed to purely biomechanical.


Holly Dale. An Exploration of the Emergence of Pattern and Form from Constraints on Growth. M.Sc. dissertation, University of Calgary, September 2014.

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