The Origin of Symmetry, Fibonacci Numbers and the Golden Ratio
A Theory of Everything
by Micah Edge
Natural Organization is a theory that explains just that, the way nature organizes itself. Born from art and the science of aesthetics, Natural Organization offers us many compelling explanations for the formation and shape of all individual structures. This web site gives an introduction to the theory and demonstrates how a simple pivotal and orbital relationship between similar sized circles may be that which governs the form and function of all objects in our Universe. The theory of Natural Organization is very simple so don’t worry; addition is the only math needed to explain it. This site deals specifically with the discoveries in Natural Organization and does not explore the subjects of Golden Ratio or Fibonacci sequence in depth. If you are not familiar with the Fibonacci sequence, use this as a reference.
Each number in this sequence is the sum of the two preceding numbers. To learn more about the Fibonacci sequence and the Golden Ratio follow the links at the bottom of the page.
Patterns in Nature
Nature is obviously using a template of sort in the formation of its many individuals. We can see this in the similar structures of unrelated subjects such as a tree, human genealogy, and a lightning bolt. Although these are three totally different things, they all utilize hierarchical organization which branches like a tree. There are many of these seemingly universal patterns which reoccur throughout the micro and macro world. For example; spirals, concentric circles, hierarchy and radial patterns occur in nature often enough to rule out the possibility of chance or coincidence. The existence of these patterns is no mathematical anomaly but an obvious systematic process of organization that occurs naturally throughout the visible Universe.
There are similarities between organic and inorganic structures.
Let us compare humans to snowflakes. It has been said that no two snowflakes are exactly alike. Yet they all have six radial points. The same could be said of humans. No two humans are exactly alike yet we all have the same basic physical anatomy, internal organs, and radial appendages. To define this phenomenon I use Infinite Variability within an Absolute Governing Structure. There are so many variables in play that all things are one of a kind, but there are usually many similar which can be categorized in groups. This does not only apply to humans and snowflakes but rather it applies to everything. Planets for example all differ from one another yet at the same time; they are all similar in structure and anatomy.
Now the question becomes how and why does this organization occur? To find the answer one must compare these universal patterns from nature in order to find out what they all have in common. So what do spirals, hierarchies, radial patterns and concentric circle have in common? In studying the ratios and proportions found in these individual structures there is a common ratio found. We call this Ratio the Golden Ratio. The Golden Ratio finds its origin in the Fibonacci sequence. Fibonacci numbers as well as the golden ratio are found all over nature and do seem to be what all these individual structures have in common. But what are numbers really? They cannot be the answer for they are after all, only numbers.
What Numbers Represent
Numbers are not found in nature. Humans have created numbers in order to abstractly represent what we find. So what do our numbers represent? Answer: In nature all things are individuals and together equal one whole individual the Universe. Similarly in math, 1 is the only number and all other numbers are multiples of this 1. So our number system is perfectly designed to represent the seemingly endless individuals that we find in nature.
Things built of things, built of things…
The Universe is the only thing that is truly one of a kind. It is the only true individual. Like us it is composed of a number of smaller pieces but on an infinitely larger scale. Organisms are composed of individual cells. The Universe is also built in this way. The largest individuals we know that the Universe is composed of are super clusters, which are composed of galaxies, which in turn are composed of solar systems, planets, molecules, atoms and so on all the way down to its most basic pieces. Perhaps this is where we can find the answers we are looking for. It would seem logical that the shape, motion and interaction of the base units “the smallest particles of the Universe" would be directly responsible for the shape, motion and interaction of all larger cooperative structures which are composed of those smallest units. Perhaps the smallest individuals of our Universe are responsible for creating the Golden Ratio that we find so prevalent in all that we see?
The Symmetrical Binary Code of Nature
When you add up any length of the Fibonacci sequence the sum is always 1 less than another Fibonacci number.
1+1+2=4 1 less than 5
1+1+2+3=7 1 less than 8
This is true no matter how far you count up the Fibonacci sequence. The sum of all the numbers together will always be 1 less than another Fibonacci number. So why not add a 1? Perhaps Fibonacci was off by 1. This again seems logical because 1+1=2+1=3. That’s three 1’s in beginning. When we add a third 1 to the beginning of the Fibonacci sequence an amazing thing happens. With the extra 1 the whole sequence becomes another Fibonacci number.
1+1+1+2+3=8 Another Fibonacci number
Even more amazing is what happens when you continue this chain or mirror it back down to the last 1. 1+1+1+2+3+2+1+1+1=13 Another Fibonacci number
In this way you can see the symmetrical anatomy of the Fibonacci number 13. This works for every Fibonacci number. Like the Universe, every Fibonacci number is composed of smaller pieces. Take the number 21 for example. If you were to break 21 into its two smaller Fibonacci numbers you would get 13 and 8. Then break those down into there smaller Fibonacci numbers. Eventually you will end up with a bunch of 1’s. When looking at a bunch of 1’s there is no discernable code or pattern, but if you group some of those 1’s into 2’s you can start to see the code of nature.
In the same way as we mirrored before, we can mirror this code as well, and it will still result in a Fibonacci number.
1 = 1
1 = 1
1 = 1
2 = 2
21 = 3
212 = 5
21212 = 8
21212 = 8
212 = 5
21 = 3
2 = 2
1 = 1
1 = 1
1 = 1
This symmetrical binary sequence can be applied to any two neighboring Fibonacci numbers.
If you arrange any two neighboring Fibonacci numbers together in the same fashion as the 2’s and 1’s, the sum of all when added together will always equal another Fibonacci number. It seems to work in a combination of “whole steps” and “half steps” in this order 21212 “whole step” and 212 “little more than half step”.
At this point numbers tend to fail those who are more visual or artistic in nature so we will replace numbers with circles. If you exchange these numbers with circles you can begin to appreciate the aesthetics hidden within their ratios.
Natural Organization Circle Maps
This image is a view of 212122122121221221212 which is equal to 34.
The next image is the next step. Now some of the 2's and 1's will be grouped by 3.
Now some of the 3's and 2's will be grouped by 5.
Now some 5's and 3's are grouped together as 8.
Now some 8's and 5's are grouped as 13.
A 13 and an 8 are grouped as 21.
Finaly the whole sequence of numbers are circled creating 34.
The next image of Natural Organization Circle Map number 34 has the numbers included so that you can see the anatomy of this Fibonacci number.
In its purest form Natural Organization is a hypothesis on the shape, motion and interaction of the base units of the Universe. This theory offers convincing evidence that the smallest particles or “building blocks” of the Universe are circular in shape and all the same size. There is a circular gear type process which results in symmetrical cooperative structures that create Fibonacci numbers, and subsequently exhibit the Golden Ratio. In this theory 1+1 only equals 2 when motion is not part of the equation. Motion is what enables interaction to occur between individuals. Without motion everything would remain as it originally was, stagnant and without growth or evolution.
Circles in Motion
The Process of Natural Organization: 1+1=3
When a circle spins on its center axis, one side will go up and the other down creating two opposing directions.
In this way, motion may be the origin of opposites. As the circle spins it may attract or repel another spinning circle depending on which way the other is spinning. If the two circles are spinning in the same direction they will offer only friction and will repel one another.
If the two circles are spinning in opposite directions they attract one another.
When two opposite spinning circles come to meet each other they work together without fighting each others direction and form a synergetic and cooperative relationship.
As they spin together, one circle will start rotating around the other perhaps sparked by the momentum of the original impact. One acts as the pivotal individual while the other acts as the orbital individual. In this way 2 circles occupy the area of a chain of 3 circles.
As the cooperative structure grows it occupies more space, seeming to reach out into the surrounding environment in order to interact with even more individuals. The cooperative structure finds another circular individual and the process continues. In this image, two circles rotate around the one so that three circles equal a chain of five.
The process of accumulation seems to follow the Fibonacci sequence and is accelerated exponentially by the structures growth. The cooperative structure will attract two more circular individuals and the pivotal axis of the entire structure moves between the two central circles.
The process continues next attracting three, then five, then eight, then thirteen circles and so on. Because the resulting patterns are symmetrical, you can rotate any of the codes on its center axis which results in Concentric Natural Organization Circle Maps.
When you combine these individual Concentric Circle Maps it results in what I find to be the most aesthetic view of the process. This is Natural Organization Concentric Circle Map 13.
See the next page Natural Evidence, to learn what these circle maps have in common with humans, plants, animals, crystal structures, and celestial bodies.
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