Stefanie Crystal

Professor Golé

Discovering Mathematics

Project #2, Phyllotaxis

4/30/99

The presence of spiral patterns in flowers and other plants such as cacti and pinecones is known as phyllotaxis. Most flowers that exhibit spiral patterns form two families of spirals; the numbers of which usually correspond to numbers found in the Fibonacci sequence. Some flowers that are found in several locations on the Smith campus display these spiral properties and can be observed to learn more about patterns naturally occurring in nature. This project involved using a digital camera to take photographs of many different flowers in the Plant House and Capen Gardens. The computer program Adobe Photo Deluxe enables the user to magnify these flower photographs and study their spiral patterns.

To operate the computer program, the user must download the digital images from the camera to the computer. In this case, the photos were posted on the Internet, and later saved in a personal file. They are then opened in the Photo Deluxe Program, where they can be trimmed and magnified in order to allow the user to have a close-up view of the spiral patterns in the center of the flowers. Once the flower‚s image is magnified, the two families of spirals are highlighted using a brushing tool. The numbers of spirals in each family often are found to be pairs in the Fibonacci sequence. The spiral patterns found in the pinecone pattern, for example, resulted in a pairing of eight spirals and thirteen spirals, both of which are members of the Fibonacci sequence.

My experience with studying these spiral patterns involved examining several different types of flowers and plants. While all of the digital photographs I took exhibit signs of spiral patterns, not all of them are easy to discern. This fact limited the amount of spiral patterns I was able to observe. Therefore, my actual drawing and counting of the spiral patterns consisted of only three separate photographs. I examined each one to find both the clockwise and counterclockwise spirals, which can be seen in the included photograph print outs appended to this paper.

In my exploration of the photographs, I found that both directions of the yellow flower contained twenty-one spirals. As stated above, the pinecone had spirals of eight (counterclockwise) and thirteen (clockwise). For the cactus, I found the spirals to be sixteen (clockwise) and twenty-six (counterclockwise). I did expect each plant to exhibit spirals following the Fibonacci sequence, and while some of them did contain pairs in the sequence, others did not. It is possible that they belong to the small percentage of flowers and plants that are not confined to this particular phenomenon.