Register for an account


Enter your name and email address below.

Your email address is used to log in and will not be shared or sold. Read our privacy policy.


Website access code

Enter your access code into the form field below.

If you are a Zinio, Nook, Kindle, Apple, or Google Play subscriber, you can enter your website access code to gain subscriber access. Your website access code is located in the upper right corner of the Table of Contents page of your digital edition.

The Sciences

Fibonacci Cactus

By Alex StoneJuly 8, 2004 5:00 AM


Sign up for our email newsletter for the latest science news

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.

3 Free Articles Left

Want it all? Get unlimited access when you subscribe.


Already a subscriber? Register or Log In

Want unlimited access?

Subscribe today and save 70%


Already a subscriber? Register or Log In