The mathematics of form and pattern applied to plant phyllotaxis

Much work has been done over the last 160 years on the subject of plant phyllotaxis. The papers by Skimper and the Bravais brothers in 1830 reveal that the arrangement of leaves on the stems of plants is highly regular. The modes of phyllotaxis can be characterized by two numbers which predominantly are from the Fibonacci series. Based on the minimization principles discovered from previous work, a mathematical model is proposed in this dissertation to encompass all of the phyllotactic modes with a very small number of assumptions and parameters.;The Model of Two Self-avoiding Morphogens which is proposed herein to explain the phyllotactic patterns has several attractive features: its simplicity, inclusiveness, and biological plausibility. It is well-known that molecules which contain an extracellular component which binds to the surfaces of epithelial cell sheets and containing and intracellular part plays a role in the signaling pathway with the DNA.;In particular, the model will explain some of the seemingly mysterious observations of phyllotaxis cited in Jean's book (Phyllotaxis: a Systemic Study in Plant Morphogens), where the number of primordia is equal to seven and the divergence angle is equal to 51.4286...