"the Fibonacci sequence"
How does this relate to the original question?
Not snark really want to know.
Thanks
A_E
Fractal Geometry is the concept where it seems that a shape repeats itself over and over within the paramaters of the same object on the atomic level. You can look this stuff up even on Wikipedia it will probably give you better difinitions than I, but it is the seemingly repeatable sequence of the same pattern that makes up all living things. The Fibonacci sequence is the way they fall together best shown by the structure of the conch shell or things like that. It is essentially the mathematical relationship of five to one (like Pi) that forms these things.
Fibonacci numbers are closely related to
Lucas numbers Ln
in that they form a complementary pair of
Lucas sequences Un(1,−1)=Fn
and Vn(1,−1)=Ln
. They are intimately connected with the
golden ratio; for example, the
closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, ... .
Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the
Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the
Fibonacci search technique and the
Fibonacci heap data structure, and graphs called
Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings,
[10] such as branching in trees,
phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a
pineapple,
[11] the flowering of an
artichoke, an uncurling
fernand the arrangement of a
pine cone's bracts.
[12]
The above is a over-view pasted from Wikpedea. This deserves a lot more research and attention. How does this apply to the naturalistic style??? The Fibonacci sequence is at the foundation of all things, it's just the way it is. If you have a bonsai that does not work artistically you can analyze it by the traditional rules and find the reason it does not work or looks more than odd. When you are dealing with something like the Naturalistic style that in many cases does not follow the traditional rules you have to go to the rules of nature to find the answers, there you may encounter the Fibonaccu sequence.