# Seeking Explanations for Plant Fibonacci Spirals

The spiral patterns on an artichoke are enough to make a physicist choke. How do plants like cacti, sunflowers, strawberries and artichokes produce geometric patterns of left- and right- handed spirals? Why do these spirals follow a mathematical rule called the Fibonacci sequence? A new theory suggests that it is the optimal energy arrangement for a structure of elements built on a conical form.

An article in PhysOrg explains the theories of three physicist/mathematicians at the University of Beijing. They were able to produce Fibonacci spirals on conical microstructures. Their investigation suggests that “plant patterns might be modeled by mutually repulsive entities for both spherical and conical surfaces.” Even so, they have not been able to come up with a mathematical proof, for good reason:

“The patterns on a sphere are now referred to as the Thomson problem, which has been generalized as the Generalized Riesz Problem,” [Zexian] Cao said. “There is no general method to find the least energy configuration for a given confining geometry, and the numerical solutioncosts enormous time of both the computers and the scientists.Even worse, it is difficult to make oneself believe that the least energy solution he finds is really the global minimum. And numerical solutions would never be accepted as proof.”

Cao said the difficulty of explaining this phenomenon is an “embarrassment” in physics. The latest explanation also fails to show a causal connection from the way DNA translates proteins into the way they become arranged at the leaf tip.

See comments from 01/21/2003 and 11/20/2003. Today’s article shows this is still an ongoing problem four years later.