Wednesday, May 25, 2016

complexity beyond the fibonacci sequence

thesciencexplorer |  Sunflowers have long been included with pineapples, artichokes, and pine cones as one of nature’s stunning examples of the Fibonacci sequence — a set in which each number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, ...). 

The numbers appear on the giant flower’s head, where the seeds arrange themselves in spirals. Count the spirals turning clockwise and counterclockwise and you will usually find a pair of numbers that sit side by side in the Fibonacci sequence.

Alan Turing first speculated sunflower seedheads adhered to the Fibonacci sequence, but sadly died before accumulating enough data to test his theory.

Four years ago, the Museum of Science and Industry in Manchester, UK picked up where Turing left off. Data on sunflower diversity were lacking, so the museum crowdsourced the problem. Members of the public were invited to grow their own sunflowers and submit photographs and spiral counts.
In a study just published in the journal Royal Society Open Science, researchers who verified the counts on 657 sunflowers provided by citizen scientists reported that one in five flowers did not conform to the Fibonacci sequence.
Some of the non-conforming seedheads approximated Fibonacci sequences, and others approximated even more complex mathematical patterns.
These exceptions to the rule have peaked the interest of the researchers, who wrote: “this paper provides a testbed against which a new generation of mathematical models can and should be built.”