A Max-Min Principle for Phyllotactic Patterns

Abstract. An interesting phenomenon about phyllotaxis is the divergence angle between two consecutive primordia. In this paper, we consider a dynamic model based on Max-Min principle for generating 2D phyllotactic patterns studied in [2, 5]. Under the hypothesis that the influence of the two predecessors is enough to fix the birth place of the new generated primordium, analysis and numerical experiments are conducted. We then propose a new measurement for evaluating the pattern uniformity (sparsity) of different divergence angles. It is found that the golden angle gives very good sparsity but there are other angles give even better sparsity under our proposed measurement.