This Article: (8 Pages)
- 1. Honey Bees challenge Evolution
- 2. Bees are Irreducibly Complex
- 3. Non-Reducible Interdependence
- 4. Arguments for Intelligent Design
- 5. Intelligent Design Supports a... Creator's Existence
- 6. Design and Nature: by a qualified... Architect
- 7. The Golden Ratio in Plants
- 8. The Golden Ratio an argument for... design in nature
7) The Golden Ratio in Plants
The leaves along a branch rotate to allow the maximum exposure to sunlight and rain. This tendency in the growth of petals or leaves is called phyllotaxis. They tend to rotate around the stem in Fibonacci ratios.
Pineapples show this feature. Each hexagonal lump on the surface is part of three different spirals. It has been shown that new leaves on a plant advance at roughly the same angle each time and this angle is 137.5 degrees, which is the angle formed by the golden ratio. It has been shown that to most efficiently close-pack points the best arrangement is in opposing spirals based on 137.5 degrees such as that shown by the the sunflowers florets.
The number of spirals formed by florets of the sunflower, following this angle, most commonly are 34 one way and 55 the other. Even if the number of spirals varies they are all in numbers found in the Fibonacci series. The number of petals on daises, 13, 21 or 34 are also in the Fibonacci sequence. The position of the petals of a rose are located by angles that are based on a fraction of the golden angle. If they grew at an angle that was a simple division of 360 degrees then at some point a petal would end up opposite and gaps would open up. The fact that the golden angle will never precisely meet itself as it rotates, or in other words its irrationality, means that it produces close packed circular structures most efficiently.
Self Similiarty
It is not just plants that grow using 'self-similarity', mollusks do also. By using a logarithmic spiral that can be inscribed in a rectangle formed by a the golden rectangle the spiral always looks the same. It seems the stars of galaxies also form comparatively flat logarithmic spirals, which is curious, as it seems they should not retain spiral shapes. Of passing interest is that Falcons also use the spiral to attack their prey, to maintain speed while keeping their prey in sight out of the eyes which are on the side of their heads. This seems a logical behaviour of optimisation. Whereas the Falcon may have an intelligence to learn this behaviour, the optimisation in the structure of plants, mollusks, and galaxies seems an inherent and inexplicable property.
Livio (2002) asks the question, “why are the successive leaves separated by the golden angle?” He points out it has been shown this is the most efficient. But this is not a reason why something happens. Livio quotes researchers who in studies generating patterns, found that where there is 'self-similarity' in growth of structures there is a limit to the number of different types of structures. Again, there may be a limit to the number of structures, but the plants and mollusks seem to have 'chosen' their specific structure above the infinite possibilities of other structures. Livio also reports recent experiments with charged oil drops randomly dropped eventually formed this pattern, and researchers have suggested that this phenomena could be caused by minimal energy states for a system of mutually repelling buds.
They don't know why the buds repel, or in other words, they still do not know what causes this phenomena. The explanation for the location of petals based on the charged oil drop experiment, which suggests that the location is determined by mutually 'repelling' buds, ignores the fact that perfect repulsion would leave the new bud as far away as possible from the previous bud, or directly opposite, not at a fraction of the angle of 137.5 degrees about their centre. In the oil drop experiment they used magnetic forces and they had to wait for the pattern to emerge. In the plant and mollusk, from their very first growth the pattern is there.
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