There is a very close connection between relatively simple math and the way most of nature is formed. Now, for those of you who don't like math, I sure hope you'll read on anyway, because this is truly fascinating stuff, and the math is quite simple.

Last year I attended an art school for a year, learning some basic art technique and history. Among the things we learned about was the Golden Section (GS), which I also had learned about earlier, but now we got to use it in real life.

For those who don't know what the Golden Section is, I'll explain it very briefly: The golden section divides a line (or anything, really) in two parts, so that the smaller part's relation to the bigger part equals the bigger part's relation to the whole. An illustration:

XXXXXXXXXXXXXZZZZZZZZ

This line is divided approximately so that the X part is as much longer than the Z part as the whole line is longer than the X part (proportionally). In math equation (sorry, math allergics, I have to be a bit technical now, so you should close your eyes for a while now, and we'll get back to the wonders of nature shortly), this would be:

X/Z = (X+Z)/X

This ratio number, called Phi, is 1,618034... So, X is 1.628034 times longer than Z, and the whole line is 1.618034 times longer than X. If you divide 1 by this number, you get 0.618034... (that's one of the beautiful things about this number), and this is called phi (with a small p).

Well, after being a bit into GS and Phi for some time, I watched a pop science program on TV (for kids, actually, but interesting nonetheless), where some professor told about the Fibonacci series. I had heard of this before, too, but didn't know much about it. Here's a brief explanation:

The Fibonacci series is a row of numbers, starting with 0 and 1, and with each successing number being the sum of the former two, like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...

The professor then told that there's a very close connection between the Golden Section and the Fibonacci series. If you divide a number in the series with the previous, you get a number close to Phi (or phi if you divide a number with the following), and the further out in the series you go, the closer you get. (3/2=1.5, 5/3=1.67, 8/5=1.6, 13/8=1.625 ...)

Well, now we head back to nature, plunging into the forest. Pick up a cone of pine, and notice that the "shells" (I don't know what they're really called) are organized into two spirals, one clockwise and one counterclockwise. Probably, you'll find that one spiral has 8 arms and the other 13.

Now let's go out in the sunflower field and study how the seeds are organized in the middle of the flower. Here, too, you'll find that they're organized in two spirals, but with a much higher number of arms in the spirals. But the number of arms will still be Fibonacci numbers.

Study any plant, and you're likely (likely, but not certain) to find the following phenomenon in some form: A leaf grows out from the stem in a certain angle. The leaf above grows at another angle, and so the leaves are distributed around the stem as you count your way upwards. After a number of rounds around the stem, and after a number of leaves, the next leaf grows in the same angle as the one you started with. You'll then have counted, for instance, 8 leaves, going 5 turns around the stem. If you count the other way, you'll probably go 3 turns. These three numbers (the number of leaves and the number of turns each direction) will be consecutive Fibonacci numbers. The advantage of this, is that each leaf is placed as far away from the others as possible, both in rotation and height, thus assuring that each leaf gets as much light as possible without blocking the light for other leaves.

There are many other examples. Spiral sea shells, petals, branching, cacti (plural cactus)... Go look for some!

How's all this done? Well, if you divide a circle's 360 degrees by Phi, you'll get a "golden angle" -- about 222.5 degrees. Biologists have found that new cells in the "growing zone" on the tip of plants often are rotated 222.5 degrees from the last cell generated. This angle lies buried in the genetics somewhere, and is reflected by the integer approximations that is the Fibonacci numbers that we find in nature.

I believe in God, and the more I learn about the mechanics of nature, the more awe-struck I am by its beauty, complexity and simplicity. For me, it does not make God smaller, it makes Him bigger. What an engineer!

I have supplied a link to a web site that can explain this in much more entertaining and professional ways, and encourages everyone to pay it a visit.

Travholt.