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To Grow, Plants Do the Mathematics

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Hormones control Fibonacci patterns

genetics, biology, botany, University of Arizona, mathematicsYou see them in sunflowers and artichokes. The familiar, concentric spiral-shaped Fibonacci sequence is part of a lot of flowering plants. These patterns precisely follow the Fibonacci sequence (1, 1, 2, 3, 5, 8), in which each digit (once you move along) is the sum of the previous two. But until now, nobody really knew how plants knew to make these mathematically precise patterns.

Researchers did know that the Fibonacci sequence provides one of the best ways for plants to maximize exposure for sunlight and other nutrients—seeds and flower steps are packed in the most efficient way possible. But scientists at the University of Arizona discovered, at least among sunflowers, that a plan growth hormone called auxin is responsible for creating the Fibonacci spirals.

Matthew Pennypacker and Alan Newell reported in Physical Review Letters that as sunflowers grow, their seeds in the head of the flower align themselves in annuli, which are closely arranged as the familiar spirals. The annuli shrink as the plant head grows and the spiral is formed. What’s causing the pattern? The researchers found that concentrations of auxin were highest right where seeds were about to be formed. So it was the auxin that led the spiral pattern formation. The researchers used a computer model that accurately predicted where auxin concentrations were going to be greatest—and how the patterns were formed.

Auxins were the first plant hormone to be discovered, and are involved in transforming stem cells into mature cells, as well as guiding the cell elongation process in plants. Since auxins are found in a wide variety of plants, the research suggests that these and other mathematical formulas may be behind many other plant growth patterns.

Source: ScienceNOW, Physical Review Letters

Photo: Wikimedia Commons

Pennybacker, M., & Newell, A. (2013). Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing Physical Review Letters, 110 (24) DOI: 10.1103/PhysRevLett.110.248104

fibonacci plants,growth patterns in plants,spiral fibonacci

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