Fibonacci Cactus

By Alex Stone|Thursday, July 08, 2004

The famous Fibonacci sequence, a series of numbers in which each is the sum of the preceding two (1, 1, 2, 3, 5, 8, . . .), shows up everywhere in nature—in nautilus shells, in pinecones, and now in the structure of cacti.

Courtesy of Patrick Shipman

Mathematician Alan Newell of the University of Arizona in Tucson and graduate student Patrick Shipman studied cacti to determine why this pattern is so ubiquitous. The researchers analyzed the plant’s shape, the thickness of its skin, and a host of other biomechanical constraints that steer its growth. When they plugged the data into a computer they discovered, to their surprise, that the most stable configurations inherently follow a Fibonacci-like form. “We show that energy is minimized by this relation,” Shipman says. He expects that similar sequences may show up in human biology as well. Applying mathematical models of pattern formation to medical problems, he suggests, could provide fresh insights into processes such as tumor formation and bone growth.

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