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Phyllotaxis Dynamics

The arrangement of leaves on a stem, wrapped tightly in intricate spiral patterns as the plant develops, can seem a random thing. It isn't. The phenomenon even has a name. Phyllotaxis.

Luke Grecki studies this. 

Luke Grecki

For his Hampshire Div III project, "Phyllotaxis dynamics: A study of transitions between plant patterns," Grecki worked with Smith College professor of mathematics Chris Golé in creating computer simulations based on mathematical models of phyllotaxis, seen not only in leaves but throughout nature in a variety of simple, repeating patterns.

"Over the last 100 or so years people have been trying to understand this, looking at the spacing and patterns geometrically. Mathematicians and physicists have formulated some rules about it, and biologists are trying to understand the physiological basis that's responsible for these rules, the chemical and mechanical structures," says Grecki. "By observing it microscopically you can understand more subtle things that happen, how patterns transition from one to another, and why certain patterns are more predominant than others."

Grecki, whose initial focus was on creative writing, became seriously interested in mathematics after taking a course with Golé. The experience influenced him so much that he asked to work with him on additional research work outside of class.  It was then that Grecki was introduced to phyllotaxis, which he eventually decided to make the focus of his Div III. The central part of it is a program he wrote that simulates different phenomena of phyllotaxis, which Golé and his colleagues use to form new hypotheses.

Grecki credits his Div III chair, Hampshire mathematics professor Ken Hoffman, with giving him important advice as he developed his project. He also says the Hampshire philosophy, as well as the Five College consortium, enabled him to explore numerous disciplines before focusing on mathematics.

"I definitely had a great time, I was exposed to a lot of great people and took advantage of the Five Colleges," says Grecki.

After graduating from Hampshire, Grecki plans to study applied mathematics at the University of California Davis.

"I'll be working on things in the same general scheme, pattern discovery and recognition," says Grecki. "And I hope to study more general features of all of these complex systems that you see in nature."

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