The Fibonacci Force
1. There are pictures which show the spiral patterns created by a sequence of growth such as that of the leaves along a branch. These patterns are usually, if not always, based on numbers or pairs of numbers in the Fibonacci series such as 8, 13. It has been noticed that the 8, 13 spirals look the same so that a pine cone and the leaves on a monkey puzzle tree have similar spirals. A picture which shows an 8, 13 pattern of growth can be called a Fibonacci field.
2. A Fibonacci field embodies a whole series of other spirals based on the Fibonacci numbers from 2 on. Each of these other spirals is developed from a set of rules common to all Fibonacci spirals and each also typical for a given Fibonacci number. These spirals are all logarithmic spirals.
3. Besides these spirals there is another pattern in a Fibonacci field created by joining together with lines, not curves, eight sequential points. This pattern is the growth pattern and its basic form is the same in all Fibonacci fields.
4. There is another set of patterns in all Fibonacci fields created by joining together in a circumference all the points on a Fibonacci spiral which are the same number of turns distant from the pole of the logarithmic spirals - the center of the Fibinacci field. There is one circumference for each turn of a set of spirals and each circumference is the same as the one before but larger and rotated a precise amount in a clockwise direction.
5. These facts about the Fibonacci field at once suggest explanations for all the many occurences in Nature of Fibonacci numbers or logarithmic spirals. For instance a flower with 3 sepals, an 8, 13 pattern of florets and a corolla of 21 petals may be understood as a Fibinaccu field which contains the 3, 8, 13, and 21 spirals. These spirals have created circumferences which are coinciding with different MADS layers so that different MADS layers are activating different numbers of growth points. In other words, the existence of different Fibonacci spirals with associated growth points and circumferences within one Fibonacci field accounts for the combinations of different Fibonacci numbers often visible to the naked eye within one organism.
Or to take another example, the angles between the arms of starfish are easily understood as 137.5 if we apply the growth diagram. This diagram shows us that the growth pattern is not 1, 2, 3, 4, 5 nor is it 1-5 all at once. The pattern is 1,3,5,2,4 - in this pattern the angle between successive arms is always 137.5. We see that the arm we call arm 2 when we think of the arms as forming a circle and which we might say is 52.5 degrees beyond arm 1 is really the 4th arm and is 412.5 degrees beyond arm 1 on a logarithmic spiral. The octopus may be explained the same way - its growth pattern is 1,4,7,2,5,8,3,6.
It is easy to see that circles and laws associated with circles and other cuts through conic sections do not explain those natural phenomena always associated with Fibonacci numbers or logarithmic spirals (shells, horns, claws, thorns, flower designs, pine apples and pine cones) whereas the Fibonacci field and its associated patterns do explain them.
6. Fibonacci numbers and logarithmic spirals are the obvious explanation for growth in nature for all three are characterized by repetition of form on a an ever larger scale. But Fibonacci numbers and log spirals are not proposed as an explanation because growth is a motion and there is no known force which would cause motion in logarithmic spirals. The forces isolated by Kepler, Newton and Maxwell are forces which move along pathways which are cuts in a conic section, not logarithmic spirals.
7. The best thing to do, since the motion exists, is to propose a "Fibonacci force" which causes these motions. The force would be centered in the pole of every logarithmic spiral in Nature and all growth in Nature would be a logarithmic spiral of one kind or another. The apple grows because of the Fibonacci force; the apple falls because of gravity.
8. The most likely source of this force is the chromosomes which are composed of a double helix, a type of spiral, though not a logarithmic spiral.
2. A Fibonacci field embodies a whole series of other spirals based on the Fibonacci numbers from 2 on. Each of these other spirals is developed from a set of rules common to all Fibonacci spirals and each also typical for a given Fibonacci number. These spirals are all logarithmic spirals.
3. Besides these spirals there is another pattern in a Fibonacci field created by joining together with lines, not curves, eight sequential points. This pattern is the growth pattern and its basic form is the same in all Fibonacci fields.
4. There is another set of patterns in all Fibonacci fields created by joining together in a circumference all the points on a Fibonacci spiral which are the same number of turns distant from the pole of the logarithmic spirals - the center of the Fibinacci field. There is one circumference for each turn of a set of spirals and each circumference is the same as the one before but larger and rotated a precise amount in a clockwise direction.
5. These facts about the Fibonacci field at once suggest explanations for all the many occurences in Nature of Fibonacci numbers or logarithmic spirals. For instance a flower with 3 sepals, an 8, 13 pattern of florets and a corolla of 21 petals may be understood as a Fibinaccu field which contains the 3, 8, 13, and 21 spirals. These spirals have created circumferences which are coinciding with different MADS layers so that different MADS layers are activating different numbers of growth points. In other words, the existence of different Fibonacci spirals with associated growth points and circumferences within one Fibonacci field accounts for the combinations of different Fibonacci numbers often visible to the naked eye within one organism.
Or to take another example, the angles between the arms of starfish are easily understood as 137.5 if we apply the growth diagram. This diagram shows us that the growth pattern is not 1, 2, 3, 4, 5 nor is it 1-5 all at once. The pattern is 1,3,5,2,4 - in this pattern the angle between successive arms is always 137.5. We see that the arm we call arm 2 when we think of the arms as forming a circle and which we might say is 52.5 degrees beyond arm 1 is really the 4th arm and is 412.5 degrees beyond arm 1 on a logarithmic spiral. The octopus may be explained the same way - its growth pattern is 1,4,7,2,5,8,3,6.
It is easy to see that circles and laws associated with circles and other cuts through conic sections do not explain those natural phenomena always associated with Fibonacci numbers or logarithmic spirals (shells, horns, claws, thorns, flower designs, pine apples and pine cones) whereas the Fibonacci field and its associated patterns do explain them.
6. Fibonacci numbers and logarithmic spirals are the obvious explanation for growth in nature for all three are characterized by repetition of form on a an ever larger scale. But Fibonacci numbers and log spirals are not proposed as an explanation because growth is a motion and there is no known force which would cause motion in logarithmic spirals. The forces isolated by Kepler, Newton and Maxwell are forces which move along pathways which are cuts in a conic section, not logarithmic spirals.
7. The best thing to do, since the motion exists, is to propose a "Fibonacci force" which causes these motions. The force would be centered in the pole of every logarithmic spiral in Nature and all growth in Nature would be a logarithmic spiral of one kind or another. The apple grows because of the Fibonacci force; the apple falls because of gravity.
8. The most likely source of this force is the chromosomes which are composed of a double helix, a type of spiral, though not a logarithmic spiral.
posted by wildswan at 4/15/2006 05:05:00 PM
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