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Fig 7
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| The campanula [Fig 7] provides a more complex example of mutual repulsion. It is a plant which usually bears a 5 lobed flower. There are many instances of numbers from the Fibonacci series occurring in plants. But that doesnt mean that a plant exhibiting elements in groups of 5, for instance, necessarily has a connection with the series.
Not every 5 is a Fibonacci 5. |
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| The Fibonacci 5 is irrationally symmetrical, as are all iterations of 137.5...° [see Fig 23, cyberflowers], whether or not the number of elements is a Fibonacci series number. But Fig 8 shows it is not regular as so many 5 petalled flowers are. |
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Fig 8
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Fig 9
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| Sometimes a campanula flower has 4 lobes, sometimes 6, sometimes 7. But in each case the shape formed [Fig 9] is regular, whether quadrilateraloid, pentagonoid, hexagonoid or heptagonoid. |
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| Mutual repulsion of the primordia provides an explanation to fit all cases, because flowers with different numbers of lobes appear on the same plant and share the same genes. |
Fig 10
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| In contrast with these regular shapes, Fig 10 shows iterations 4 - 7 at 137.5°. |
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| It is sure that the campanula cannot be using a perceived angle of 72° or 144° because both of these repeat after 5 iterations. Coping with one or two extra primordia, or with one fewer, is not a problem if they mutually repel one another. But an upper limit is probably not too distant. |
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Fig 11
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| The use of a perceived angle provides another morphological solution. It too had a limiting factor. The angles, however they vary as a result of differing sensitivities to light, would be acute. The first 5 iterations of 42.5...°, the supplementary angle to 137.5...°, for example, would look like Fig 11. |
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| The blackberry's answer to the problem, shared with many other plants, comes next. | |||||||||||||||||||||||||||