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** (from this link: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html )** :

Imagine 120 seeds appearing from a single central growing point. Each new seed is just phi (0·618) of a turn from the last one (or, equivalently, there are Phi (1·618) seeds per turn). No matter how big the seed head gets, the seeds are always equally spaced. At all stages the Fibonacci Spirals can be seen.

This animation was produced by Maple. If there are N seeds in one frame, then the newest seed appears nearest the central dot, at 0·618 of a turn from the angle at which the last appeared. A seed which is i frames "old" still keeps its original angle from the exact centre but will have moved out to a distance which is the square-root of i.

The same pattern shown by these dots (seeds) is followed if the dots then develop into leaves or branches or petals. Each dot only moves out directly from the central stem in a straight line.

This process models what happens in nature when the "growing tip" produces seeds in a spiral fashion. The only active area is the growing tip - the seeds only get bigger once they have appeared.

- goldenRatio_exp01.jpg:

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Attachment | Action | Size | Date | Who | Comment |
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goldenRatio_exp01.jpg | manage | 91.1 K | 04 Mar 2003 - 00:54 | HiazHhzz |

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