Patrick Shipman

Department of Mathematics
Colorado State University


Inspecting a sunower head, one may notice first the diamond-shaped seeds that tile the disk.  Families of spirals catch the eye, and if one counts the numbers of spirals in each family, one typically arrives at successive members of the Fibonacci sequence 1, 1, 2, 3, 5, 8, ...  The spiral families seem to blend into each other so that lower members of the Fibonacci sequence are observed near the center of the disk and higher numbers as one works one's way out.  Yet, there is a self-similarity in that locally the pattern is nearly the same throughout the disk.  The arrangement of elements such as seeds on a sunflower, leaves on plants, bracts on a pine cone, or aeroles on cacti, is referred to as phyllotaxis, and it has long been observed that only a few classes of phyllotactic patterns are commonly observed in nature.  The same Fibonacci-spiral pattern, for example, is commonly observed on pine cones and cacti.  Why is it that only a few patterns dominate?  And what chemical or physical mechanisms are behind the formation of these patterns?

Through mathematical models for the formation of phyllotactic patterns based on biochemical and biomechanical mechanisms, we suggest ways to understand both universal aspects of phyllotactic patterns as well as how interacting mechanisms can cooperate or compete to produce the array of patterns seen in nature. 

The Team

Alan Newell, Regents' Professor of Mathematics (University of Arizona)

Matt Pennybacker, Graduate Student, Mathematics (University of Arizona)

Patrick Shipman, Assistant Professor of Mathematics

Myla Kilchrist, Undergraduate, Mathematics

Francis Motta, Graduate Student, Mathematics

Jaime Shinn, Graduate Student, Mathematics

Todd Cooke, Professor of Life Sciences (University of Maryland-College Park)