Abstract
The scale patterns of 6000 cones from one single tree of <em>Pinus nigra</em> Arn. have been examined. Apart from the main Fibonacci pattern with 8 and 13 parastichies, nine aberrant spiral patterns with Fibonacci-type sequences have been found. They are quite rare and occur with different frequencies. The parastichy quotient 8/13 of the prevalent pattern is very close to the golden ratio 0.618. In case of the black pine it appeared that the greater the deviation of the parastichy quotient <em>m</em>/<em>n</em> from 0.618, the rarer the pattern. Similar results obtained for the sample of 1506 cones collected from three individual trees of larch (<em>Larix decidua</em> Mill.) suggest a true correlation between the frequency of a pattern and the deviation of its parastichy quotient from the golden ratio.
Highlights
Material, methods and resultsLooking at European black pine cones from below (Fig. 1), curved rows of scales running in two opposite directions can be observed, one clockwise, the other counter-clockwise
Similar results obtained for the sample of 1506 cones collected from three individual trees of larch (Larix decidua Mill.) suggest a true correlation between the frequency of a pattern and the deviation of its parastichy quotient from the golden ratio
When studying Picea abies cones, Alexander Braun [6] noted in 1831 that a small minority did not show the main Fibonacci sequence, but other patterns; most often the sequences 1, 3, 4, ... and 2, 4, 6,. His early observation of the most frequent aberrant patterns was confirmed by later researchers
Summary
Looking at European black pine cones from below (Fig. 1), curved rows of scales running in two opposite directions can be observed, one clockwise, the other counter-clockwise. These conspicuous rows are called contact parastichies. There are exceptions to the rule: in most species of conifers, always quite rarely but in different frequency, aberrant patterns of cones show different parastichy numbers. They belong to the “Fibonacci-type” sequences [1]; as in the main Fibonacci sequence, each number is the sum of the previous two (Fig. 2). The aim of the present study was mainly to compare the phyllotactic diversity of one single Pinus nigra tree with pooled data of other species
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