A Model for Branch Competition
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Branching (or tip-splitting) is a ubiquitous feature of growth processes in nature. We introduce a simple model, linear in growth probabilities, of branch competition that combines tip-splitting processes, local screening, and extinction of branches whose growth has come to an end. This model admits an exact solution; which is corroborated by numerical results. An extension of the model that depends quadratically upon growth probabilities exhibits a phase transition, with non-trivial scaling in the neighborhood of that transition.
KeywordsPattern formation Multifractality Diffusion-limited aggregation Critical phenomena
I am grateful to Prof. Ray Goldstein for his hospitality during a visit to the Department of Applied Mathematics and Theoretical Physics at Cambridge University, which afforded me time to organize my thoughts on this topic.