Mechanism of Pattern Formation in Plants

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Paul B. Green 9603705 The developmental mechanisms producing shoot patterns in plants are of interest for practical and theoretical reasons. The practical side involves branching and the physical stability of the plant as well as the yield of fruit or grain, which reflects the pattern in the flower producing it. The theoretical side relates to the fact that plants show only two centric patterns: whorls as in the iris flower, and crossed spirals as in the pine cone. Why only these two, with one of them (spirals) involving the golden section (1:0.618), long known as special irrational fraction in mathematics? This grant is to further establish that the explanation lies in the physical folding of tissue that occurs to produce the lateral organ, be it a limb, petal, flower, etc., at the top of the plant. Testing this idea requires advanced mathematics, but it is in range of current engineering analytical approaches.