Fractal Cosmology


Gottfried Wilhelm Leibniz(1646 - 1716) has suggested a unique idea called “Monadology”.

He thought that the universe consists of innumerable monads and another complete universe is concealed in each of them.


To consider this idea, you might start by understanding that it represents a kind of fractal structure of the universe; when a particle contains another complete universe in it, such a universe must be again composed of much smaller innumerable particles, in each of which another smaller universe may repeat.

In a fractal structure, this process continues endlessly.


If the universe were really formed in a fractal structure, you could say our cosmos might be a particle, too.

We may be living in a particle.

Such particles as the cosmos may exist innumerably.

And there may be a gigantic universe, and it may not be the end of all there is. In fact, it might be another particle in another greater universe.

Such a process would also continue endlessly in a fractal structure.

(In this essay, the <universe> is used for a universe in the fractal structure while the “cosmos” is used for the space which we belong to)


In a universe of fractal structure, infinity is the final answer.

Infinity - not only horizontally but also vertically.

This idea may be quite sensible in terms of philosophy, but in the aspect of science, it has been impossible until now.


Now, you will see the reality of the fractal universe in this essay.

You will see the ultimate substance of matter.

And you will see here the true face of time, too.


Big Bang Theory

I am going to prove in this essay that the universe is formed in a fractal structure.

However, since the Big Bang theory is dominating today's ideas of cosmology, I think I have to mention it beforehand.


There must exist only one ultimate truth of the universe.

If the Big Bang theory were definitely true, all other ideas would not be worth consideration because we have already got the truth.

But if the Big Bang theory proves to be not true, you will have to take another idea seriously.


So, I am going to indicate here the wrongfulness of the Big Bang theory before I start demonstrations of Fractal Cosmology.


According to the Big Bang theory, a particle of ultra-high density exploded about 15 billion years ago, and since then the cosmos has been expanding at the velocity of light.

So, cosmic history is said to be 15 billion years old and the cosmic radius to be 15 billion light-years.


Since time and space are inseparably related to one another, any theory upon the cosmos has to explain cosmic phenomena logically in the viewpoint of time as well as of space.


The Big Bang is a deduction drawn from the red-shift of galaxial spectrums.

Except several members of the Local Group, all galaxies in the cosmos are concluded to be receding from us, which has been thought the only reasonable explanation for all the galaxial spectrums showing red-shift.

If the cosmos has been expanding, there must have been a starting point of expansion - that was the Big Bang, physicists have concluded.


However, if you failed to explain cosmic phenomena in terms of time by means of Big Bang theory, you would have to search for another reasonable cause of the red-shift.



In the meantime, astronomers who have observed galaxies know the following facts;


(1) There are more than 100 billion galaxies in the cosmos.


(2) Galaxies are basically forming clusters here and there; several or dozens of galaxies gather to make up a cluster.


(3) Galaxies in a cluster system are combined because of gravitation.


(4) Galaxies revolve around the total gravitational center of a cluster system.


(5) The Milky Way Galaxy is also a member of a cluster called the <Local Group> which consists of 30 or so nearby galaxies, including the Andromeda galaxy which is about 2.5 million light-years away from us.

The Amdromeda galaxy at the opposite side of the Milky Way Galaxy in the Local Group, is nearing toward us in the course of its revolution around the total gravitational center of the Local Group.


(6) The pure rectilineal approaching speed of the Andromeda galaxy is about 50 km/sec.


The total rectilineal travelling distance of the Andromeda galaxy during its one time revolution around the Local Group may be about double the distance between it and us; that is 5 million light-years.

Consequently, you can simply figure out the revolution period of the Andromeda galaxy, through dividing 5 million light-years by 50 km/sec.


5 million light-years : 50 km/sec =

= (5,000,000 ∙ 365days 4hours 60min 60sec ∙ 300,000 km) : 50 km/sec =

= 9.46 ∙ 1017 sec.


When you convert 9.46 ∙ 1017 seconds into years, it makes 30 billion years.  This means the Andromeda galaxy has not yet revolved once since the beginning of cosmic history.

It does not make sense.



However, somebody might maintain this supposition; as the cosmos had been expanding at the velocity of light, the cosmic radius was smaller in the past. Therefore, the radius of the Local Group must have been smaller, too.

In such a situation, intergalaxial gravitation had to increase to result inevitably in faster movements of galaxies.

Consequently, though they are moving slowly at the moment, they must have revolved many times already while the cosmic radius was much smaller than now.


This sounds plausible.

But let's see the reality, not the deduction.


Astronomers have observed that the cosmic structure is uniform to as far as 100 billion light-years.

This means that you can say galaxies in the cluster systems have not revolved once during at least 100 billion years.


Now, let's think about the future this time.

The cosmos is expanding in the viewpoint of the Big Bang theory.

Therefore, if the cosmic radius becomes double the present one, the extent of the Local Group will also be double the present one.


After 15 billion years when the cosmos has expanded to 30 billion light-years in radius, the extent of the Local Group should be 5 million light-years.

By then, the Andromeda galaxy may be reaching the position where the Milky Way Galaxy is presently located.


However, the Andromeda galaxy would not be able to reach there because the extent of the Local Group will become wider and wider while it travels and, to the contrary, its travelling speed will become slower and slower with the decrement of the gravitational interaction.


Though the Andromeda galaxy has reached the position where the Milky Way Galaxy was once located, Andromedans will never be able to finish a revolution around the Local Group.  That is because it will take another 30 billion years or longer to carry out another half of their itinerary.


You can tell this story at any point in the future.

Therefore, you may conclude that the Andromeda galaxy can never complete a revolution in the future as long as the cosmos expands.


Now, we have obtained two definite points in case we regarded the Big Bang theory as true; one is that galaxies in cluster systems have not revolved once during at least 10 billion years in the past, and the other is that they will never be able to carry out a revolution in the future.


Therefore, the conclusion seems to me that galaxies are not revolving.

Galaxies can not revolve if the cosmos is ruled by the Big Bang theory.


However, this is in contradiction to reality.

The reality is that galaxies are combined in gravitation and they are revolving around the total gravitational center of the cluster.

It is a reality that astronomers have concluded through observations.


Those two contradictory conclusions can not be true at same time.

So, we have to choose one of them.  We have to choose one between the reality and the deduction.

I would like to choose the reality, for I think any theory can not surpass the reality.


As the Big Bang theory failed to explain the time factor of cosmic phenomena, so it might be said to be untrue.

Now we might consider Fractal Cosmology.


Fractal Structure

In the Fractal Cosmology, the cosmos is substantially the same as a particle.

The cosmos is replicated in each particle which comprises cosmos.


As man is also a component of the cosmos, you could describe the fractal universe by laying stress on man, too.

That is, you could imagine a gigantic being in which numerous cosmoses are included, and our cosmos is just one of them, and there are numerous particles in your body, each of which may be thought to be a complete cosmos by ultra-small men who may be living in it.


If this idea were true, you might be able to prove it.

It is a question of similar figures.  I will show you a simple example.


Here is a triangle. You expand it to double the size in a duplicator.

Now you have two triangles; the one is small and the other is large.

These two triangles are similar shapes.


In similar shapes, the ratio between the corresponding sides of each other is always constant.

So, they retain a substantial identity.


When you expand the small one to double the size or reduce the large one to half the size, they will meet exactly.

There is no method to tell the difference between them.

Therefore, if two triangles prove to be similar shapes, you can regard them as retaining substantial identity.


This logic can be applied regardless of the size of triangles.


Suppose you start to expand the one larger and larger, and reduce the other smaller and smaller.

Though the large one has became larger by a million times than the small one, there will not happen any change in the fact that the two are substantially identical.


Now, let's suppose you expanded one to the size of the cosmos and reduced another to the size of a subatomic particle.

Even in such a case, as far as you are able to measure every corresponding side, you will not have any difficulty to prove them to be similar shapes.


This is a simple and unquestionable logic.

If you could measure all the elements both in the gigantic being and in your body and then show all the ratios of corresponding elements to be always constant, the idea that the gigantic being and yourself are substantially the same might be recognized as true.

This is the method to prove the fractal structure of the universe.


Stages Of The Universe

Let's call the large world inside the gigantic being 'the macro-world' and call the small world replicated in your body 'the micro-world'.

Then you can arrange all the stages of the universe from subatomic particles to the gigantic being as follows;


(1)Micro-world : subatomic particles - (atomic nucleus) - atoms - molecules - macromolecules - morphological elements - cells - man

(2)Macro-world : stars(the sun) - (galaxial nucleus) - galaxies - clusters - great clusters - superclusters - the cosmos - gigantic being


Above line-ups include all stages of the universe, and no outstanding stage exists other than above.


If the universe were replicated in fractal structure, the magnitude ratios of corresponding elements between the two extreme worlds would be all constant.


To compare the appearances roughly at each stage, you may become aware that elements in the two line-ups are likely to match each other as the sequence as arranged above.

I decided the sequence after deliberately comparing their appearances, distances between colleagues and so on.


In the above sequence, atoms correspond to galaxies.


However, you may be familiar with the idea that the atom is similar to the solar system. This idea looks rather widespread because, according to the classic atomic model, electrons have been described as turning around an atomic nucleus.

However, this idea is far from the reality.


In the material world the distance between atoms is very close; their neighbors are mostly in the range of their diameters or so.

But the distance between stars is exorbitant; stars are normally separated in the distance of some light-years which is equivalent to tens of millions of times the average stellar diameter.


Consequently, the idea that atomic structure may be similar to that of the solar system is not worth consideration at all.


Now let's pay attention to the above sequence.



By the way, it is indispensable that you must confirm each size first of all when you intend to calculate the ratio of two elements.

However, as you may easily notice, to decide the definite sizes of elements in the above line-ups is not possible.  It is because the sizes of all the elements are ranging within some extent.


For instance, galaxial diameter: 10,000 ~ 100,000 light-years

             estimation of cosmic radius: 10 ~ 30 billion light-years

             cellular diameter: 10 ~ 100 microns


Like this, every element has not a single value but is distributed within some range.


But, in the material world, things are arranged in quite fair order.

When you survey the magnitude range of members at each stage in above line-ups carefully, you may notice the fact that in general cases the upper value does not exceed 10 times of the lower value.


Now, my suggestion is that you calculate every ratio using mean values and admit a tenfold variation at each result.


Somebody may assert that comparing things of indefinite magnitudes is meaningless, but I think it's quite a fair method for dealing with the material world in which members of each stage, various as their sizes may be, are distributed within quite limited ranges.


Demonstrations In The Aspect Of Space

From now, I'm going to calculate each ratio one by one.

All data used in these demonstrations are from the findings of modern science.

The purpose of these demonstrations are, as you understand, to confirm if all ratios would be constant or not.


First, I will start with [atomic nucleus : galaxial nucleus].

The ratio of [subatomic particle : star] will be calculated in the end, for it needs some complicated explanation.


For some calculations, I'll use the mean radius of elements, the shapes of which are mostly spherical and compact.

But for some others, I'll use a mean diameter or a rough magnitude of elements, the shapes of which are mostly irregular.


(1) The atom has a nucleus at its center.

The nuclear radius is about 1/100,000 of the atomic radius, i.e. 10-13 cm.

A galaxy generally has a nucleus at its center, too, and its diameter does not exceed 1 light-year.

In case of the Milky Way Galaxy, the nuclear diameter is observed to be about 0.65 light-year.

Recently, quasars have become understood as being nuclei of active galaxies and their diameter is estimated to be no larger than 1 light-year.

Therefore, you may regard the nucleus of the Milky Way Galaxy as a standard.

Then the mean radius of galaxial nuclei can be decided as 0.33 light-year.

Radius of atomic nucleus : radius of galaxial nucleus =

= 10-13 cm : 0.33 light-year =

= 10-18 km : 3.12 ∙ 1012 km =

= 1 : 3.12 ∙ 1030


(2) The atomic radius is generally said to be 1 angstrom, i.e. 10-8 cm.

Galaxial diameters are ranging from 10,000 to 100,000 light-years so that you may take 30,000 light-years for the mean galaxial radius.

Atomic radius : galaxial radius =

= 1 angstrom : 30,000 light-years =

= 10-13 km : 2.84 ∙ 1017 km =

= 1 : 2.84 ∙ 1030


(3) There are so many kinds of molecules and their sizes so various that it is very hard to determine the mean molecular size.

To regard their shapes as spherical, small molecules are said to be ranging from 1 to 10 angstroms in diameter.


In an organism, proteins are the typical macromolecules, and they consist of amino acids.

Therefore, amino acids may be regarded as the typical molecules in an organism.

The size of amino acids in an alpha-helix, one of the typical protein structures, is about 5 angstroms.

So, you may take 5 angstroms for the mean molecular diameter of organisms.


Several or dozens of galaxies gather to form a cluster.

The typical extent of clusters is observed to be about 1.5 million light-years in diameter.

Molecular diameter : cluster diameter =

= 5 angstroms : 1.5 million light-years =

= 5 ∙ 10-13 km : 1.42 ∙ 1019 km =

= 1 : 28.4 ∙ 1030


(4) The primary organic elements in organisms are macromolecules such as proteins, nucleic acids or polysaccharides.

There are many kinds of macromolecules so that determining the mean size must be very hard, too.

Therefore, it's better to find a typical one.


Protein occupies the largest portion of an organism.

And a typical protein consists of about 200 amino acids.

So, you may say the typical macromolecule in an organism is the protein which is assembled with about 200 pieces of amino acids.

The size of such a typical protein is about 300 angstroms.

Atoms are united to make up a molecule, and molecules are combined to organize a macromolecule.

Such a process is exactly repeated in the macro-world, too.

Nearby galaxies are combined to make up a cluster, and clusters gather to form a great cluster.

The great cluster is generally formed by more than 50 galaxies, and its extent is about 10 million light-years.

Magnitude of the macromolecule : magnitude of the great cluster =

= 300 angstroms : 10 million light-years =

= 3 ∙ 10-11 km : 9.46 ∙ 1019 km =

= 1 : 3.15 ∙ 1030


(5) The actual physiological processes of the cell are performed by morphological elements such as mitochondria, microtubules, golgi bodies, etc., which are organized with macromolecules.

There are many kinds of morphological elements and their sizes are all different, but you may notice that they are mostly measurable in microns.

The mean size of them all could be said to be 5 microns.

As the tenfold variation is permitted for these calculations, most morphological elements may be covered by it.

The last stage in the cosmos is the supercluster, the same as the last stage in the cell is the morphological element.


Since 1980, astronomers have discovered superclusters, the greatest structures in the cosmos, such as Bubbles, Stakes and Great Walls.

The extent of these superclusters generally reaches some hundreds of millions of light-years.

So, you may take 500 million light-years for the mean magnitude of superclusters, which may cover most of them to consider the tenfold variation.

Magnitude of morphological element : magnitude of supercluster =

= 5 microns : 500 million light-years =

= 5 ∙ 10-9 km : 4.73 ∙ 1021 km =

= 1 : 0.95 ∙ 1030


(6) The human body consists of around sixty thousand billion cells.

The shapes of cells are generally spherical, and their sizes are mostly ranging from 10 to 100 microns in diameter.

So, you may take 50 microns for the mean cellular diameter.

Then the mean cellular radius makes 25 microns.

The cosmic radius is often mentioned differently by scientists.

Their opinions may vary but converge in ranges from 10 to 30 billion light-years, among which 15 billion light-years is widely accepted.

So, you may take 15 billion light-years for the cosmic radius.


Cellular radius : cosmic radius =

= 25 microns : 15 billion light-years =

= 2.5 ∙ 10-8 km : 1.42 ∙ 1023 km =

= 1 : 5.68 ∙ 1030


Ultra-Small Particles

(7) Now it is time to calculate the ratio of [subatomic particle : star].

Stars in the galaxial system are turning around the galaxial center, while electrons are turning, or distributed in the meaning of the quantum theory, around the atomic nucleus.

Therefore, you may regard them as corresponding to each other in fractal structure.


However, you may easily notice a great disharmony between them.

In the Milky Way Galaxy, for instance, there are more than 300 billion stars; on the other hand, there exist only a few electrons in the atom.

Hydrogen has one electron only, carbon 6, nitrogen 7, oxigen 8, and even uranium, having a very heavy atomic weight, has just 92 electrons.

Here, I am going to suggest a new idea of the electron.

As is known well, stars in the galaxial system are not scattered at random but form spiral arms.
My opinion is that electrons may carry such a figure as spiral arms of the galaxy.  
So to speak, the electron may be not a mere particle but a belt which consists of numerous ultra-small particles.

Such an idea will become clear by the following story.

Recently physicists have observed the actual radius of the electron.
It is measured to be less than 10-20 cm, while the calculated one in the quantum electric dynamics is 10-16 cm.

The observation of the actual electronic size implicates an inevitable amendment of the concept concerning the electron.

When the electronic radius is 10-20 cm, its volume is 10-60 cm3.
The electronic mass is said to be about 10-27 g.

Consequently, the mass density of the electron becomes 1033 g/cm3.

It is a universal idea that the electron is a light particle, but, by the knowledge that the actual electronic radius is less than 10-20 cm, this idea is bound to be amended.

The electron is not light.  It is heavy. It is extremely heavy.

You may compare it with the neutron.  

The neutron is said to be a heavy particle.  
Its radius is about 10-13 cm, therefore, its volume is about 10-39 cm3.  
The mass of the neutron is about 10-24 g.
Consequently, the mass density of the neutron is merely 1015 g/cm3.

Why do people say the diamond is heavy matter?  
That is because the mass density of the diamond is high.
The mass density 1033 g/cm3 of the electron is far higher than that 1015 g/cm3of the neutron, beyond comparison.

You may not say now the electron is light.  
It is very heavy, without question.  
However, why is it so heavy?  

It is impossible to explain this fact by the idea that the electron is just a particle, but it could be explained well by the idea that the electron might be a belt consisting of numerous ultra-small particles.

The electronic belt is turning slowly, i.e. in about 250 km/sec, around the nucleus.  
But, when it gets out of the atomic system, it is accelerated to the speed of light.  
In this case, all ultra-small particles comprising the electronic belt would run in a queue so that all the particles would be concentrated at a point.

Consequently, you may regard the observed electronic radius as being the radius of the ultra-small particle.  
The cause of such a high mass density of the electron is now self-explanatory.

The sun is a star of typical magnitude in our Galaxy, and its radius is about 700,000 km.

Now, you may transform [the subatomic particle : the star] into

[the ultra-small particle : the sun].

Ultra-small particle radius : solar radius =
= 10-20 cm : 7 ∙ 105 km =
= 10-25 km : 7 ∙ 105 km =
= 1 : 7 ∙ 103


Constant Number 1030

You  have now calculated all ratios of corresponding elements between the micro-world and the macro-world.  
And you may note all those are showing similar results containing a constant number of 1030.


Among them, the ratio of [molecule : cluster] is found to deviate a little from the other ones.  
It is from the difficulty in determining the mean molecular diameter, nevertheless, it is not bad to consider the tenfold variation.


Is it a coincidence?
Some fortuitists may say that any fortuity could happen.


But even an extreme fortuitist would not expect that the same fortuity might happen again and again.  
If you expected something and it has happened, it might be a predeterminate consequence, not a fortuity.


In this essay, you will see more of such inevitable consequences.


If all these were not just a series of fortuity, the universe could be said to be consecutive vertically in fractal structure, and the magnifying power between two adjacent levels of fractal to be around 1030.


So to speak, the gigantic being may be taller than you by 1030  times, and you may be, in turn, taller by 1030  times than the small beings living in your cells.  


The cosmos, though it may be a cell, looks great to you as you are living in a micro-world in the gigantic being.  
And, in turn, the small beings living in another micro-world in your cells may observe the cellular radius at 15 billion light-years by their measurement.


As a matter of fact, you can see only one cosmos, i.e. only one cell of the gigantic being, so that you are unable to know what it is.
It could be a worm, or a kangaroo.  
Nobody knows at the moment.


But in the future, if astronomers make out a perfect three-dimensional distribution map of the entire galaxies in the cosmos, we may be able to know what it is, by analyzing superclusters corresponding to DNA.
Till then, let's take it for a humanoid for the sake of romanticism.


Demonstrations In The Aspect Of Time

Another aspect of the universe as fundamental as space is time.


Physicists define time as the fourth axis and explain the universe in the concept of four-dimensional space.  

It is quite questionable whether time is a real axis, but I'm not going to express my subjective view of time here.  


I'm just going to demonstrate the reality of time in a fracral structure of the universe.

I hope you will see the true face of time eventually.


(1) The differentiated time:


As you may note, the logic of the Fractal Cosmology is very simple.
The principle of time ruling the fractal universe is simple, too.


However, you may be required to open your mind to accept the simplicity.
When you are prejudiced, you may fail to catch the plain reality.
So, I sincerely ask you to open your mind widely beforehand.


I will give you an example for an easier approach to the principle of time.
Let's suppose here is a ground with the 100 meters track and a man of 1.8 meters high is about to dash forward at the starting line.
Say he can run 100 meters in 10 seconds.


And now, imagine a world where every size has been shrunken to 1/10 by a miraculous magic.  
In that small world, both the man and the ground have shrunken in the same ratio, therefore, the shrunken track will look unquestionably as 100 meters to the shrunken man.


Now, let's position the starting lines of both grounds on a line, and let the two men dash toward each goal line at the same time.


In such a situation, the shrunken man will naturally see it passed 10 seconds by his watch when he has reached the goal line, for in his world he himself, the ground and all other surroundings have shrunken in the same ratio, and, his watch will also show the time of the shrunken world.


However, when you see the shrunken ground, the length of its track will look, as a matter of course, to be 10 meters.
Consequently, the runner in the normal world will pass the same point as the end line of the shrunken track in one second.


Supposing the two runners could see one another, the normal runner would see busy strokes of the shrunken runner, and, the latter would see a giant taller than himself by 10 times running in a very slow motion as if replaying a video film slowly at 1/10 speed.


The cause of such phenomenon is that the flow of time changes in proportion to the change of space scale.  
So to speak, a man living in a world shrunken to 1/10 may feel the flow of time slower by 10 times.


To express accurately, one second of the normal world will be experienced just like 10 seconds by the man in a world shrunken to 1/10 scale.


Here, a point to pay attention to is that the slow flow of time does not mean the real length of time becomes longer, but means the flow of time becomes so differentiated for the man in the shrunken world that he will simply experience it slower.


The principle of such a story can be applied in the same manner to any case even if the scale of space changes to 1/100, 1/1,000, or further, 1/1030.

If the universe were really repeated in fractal structure in the ratio of [1 : 1030], the flow of time would change in the same ratio, too.


Therefore, even if a long period of 1030 seconds have passed in our world, the clock of the gigantic being would tick only once; in the other hand, a second of ours would be differentiated to 1030 seconds for the small beings living in the micro-world.


This is the principle of time in the fractal universe.
However, can it be proved?


The Secret Of Time

(2) The secret of time:


The secret of time is concealed in the motion of galaxies.


Look at the pictures of galaxies again.
They look just like a still image of a furiously rotating object.


As you know, the galaxy is rotating around its center.  
It takes about 200 million years for a galaxial rotation.  
Why does it take  so long despite their quick appearances?  

It is because we are actually in a micro-world inside a cell of the gigantic being.


As 1030 seconds pass in our world during one second of the gigantic being, so, even 200 million years must be nothing but a fraction of moment for him.  

Since he will recognize the galaxies as atoms, he will consider the galaxial rotation period as the atomic rotation period.


The universe is so replicated in the same ratio at each fractal level that the atomic rotation period he will measure must be just the same as the period we measure from the atom.


Now I'm going to calculate the atomic rotation period on the basis of the principle of time of the Fractal Cosmology.


You may probably think my intention as absurd because you know such a subject belongs to the field of quantum theory.
However, you will come to realize that any cosmic phenomena can be interpreted logically by Fractal Cosmology.


In Fractal Cosmology, the flow of time changes in proportion to the change of space scale.
Therefore, the ratio of the atomic rotation period to the galaxial rotation period can be described as below;


Atomic rotation period : galaxial rotation period =
= atomic radius : galaxial radius


You know already the ratio of [atomic radius : galaxial radius].
And you may take 200 million years for the galaxial rotation period.


Actually the galaxial rotation period varies to the position in the galaxial system, but, to consider the tenfold variation, the period of 200 million years may cover any case regardless of the position.


Consequently, the above formula can be arranged as below;


x : 200 million years = 1 : 2.84 ∙ 1030
x : 6.31 ∙ 1015 seconds = 1 : 2.84 ∙ 1030
x = (6.31 ∙ 1015seconds) : (2.84 ∙ 1030)
= 2.22 ∙ 10-15 second


According to the calculation based on the principle of time in Fractal Cosmology, the atomic rotation period is 2.22 ∙ 10-15 second.


Then, let's compare this result with the data of physics.


Niels Bohr, a Danish physicist and Nobel Prize winner, is famous for having applied the quantum theory to the study of atomic structure for the first time.

His theory, though classical, agrees exactly with the actuality when applied to the hydrogen atom.


When Bohr's formula is applied to the hydrogen atom, the rotation frequencies per second in case of quantum number 2 are 8.2 ∙ 1014 times, from which the rotation period is calculated to be 1.22 ∙ 10-15 second.


Compare the two results.


For your reference, the atomic rotation period varies to the quantum numbers.
Quantum number 2 corresponds to the parts of visible rays in the atomic spectrum.  
Since the galaxial rotation was observed through visual rays, you have to consider the case of quantum number 2.

And, the rotation period varies a little to the kind of atom, but such differences are quite negligible in this comparison.


The amazing agreement between the results from the physical theory and from the Fractal Cosmology proves the validity of this new Cosmology.


The universe is replicated in fractal structure, and the flow of time changes in proportion to the change of space scale.

This may be the very secret of time and space that mankind has long wished to know.


Molecular Vibration

(3) The molecular vibration and the movement of Andromeda galaxy:


As the Fractal Cosmology is based on the irresistible logic of facts, you can apply it to any case of the universe as far as appropriate data are available.


Now I'm going to introduce you one more case confirming this new theory.

A molecule normally consists of several atoms, which are combined by interatomic attraction.


Several or dozens of neighboring galaxies form a cluster.
The force to make up such a system is the gravitation of galaxies.


As the molecule corresponds to the cluster of galaxies in the Fractal Cosmology, the cycles of some particular motion of the two systems can be anticipated to show the ratio of [1 : 1030].


In the molecular system, atoms are vibrating to one another and, at the same time, they are turning around the center of total attraction.
For the molecule, vibrations take place typically 1013 times per second and rotations 1011 times per second.


These molecular motions vary, of course, to the kind or the phase of the molecule, but you may regard the typical ones as valid enough to compare with the macro-world, to consider the tenfold variation.

Therefore, the molecular vibration period makes 10-13 seconds and the molecular rotation period 10-11 seconds.

When you compare the two molecular motions, you may note the fact that vibrations are taking place faster than rotations by 100 times.
Atoms turn once around the center of total attraction while they vibrate 100 times.

This is to say, they move around little by little every time they vibrate once, and complete one rotation after vibrating 100 times.

Therefore, if you could watch the molecular motions by your eyes, you might notice only vibrations to be outstanding.


Clusters of galaxies are so far from us that precise measurements of the relative galaxial motions to each other in the clusters are almost impossible to perform.


The only cluster from which you can obtain such valid data may be the Local Group which our Milky Way Galaxy belongs to.
Since the Local Group is not a peculiar cluster in the cosmos, you may regard its motions as standard.


Galaxies in the cluster system are revolving around the center of total gravitation.
Andromeda galaxy located at the opposite side in the Local Group is nearing us at 50 km/sec, which astronomers interpret as the motion of its revolution.


In a fractal structure of the universe, clusters of galxies correspond to molecules, therefore, galaxies in the cluster system should be not only revolving but also vibrating as well as atoms are doing in the molecular system.


In such a case, vibrations will take place faster than revolutions by 100 times so that galaxial momentums you can measure must be mostly out of the motion of vibration.
Consequently, you may regard the approaching speed of Andromeda galaxy as its vibrating speed.

The Milky Way and Andromeda galaxies are the central ones at either part of the Local Group.
The fact that the Andromeda galaxy is approaching toward the center of the Milky Way implicates the latter also approaching toward the former.
Therefore, the Andromeda galaxy will come nearly to the center of the Local Group and go back to the present position to finish a vibration.

As the distance between these two galaxies is about 2.5 million light-years, the travelling distance of Andromeda galaxy during its one time vibration will make also about 2.5 million light-years.


Now, you can figure out the vibration period of the Local Group through dividing 2.5 million light-years by 50 km/sec.


2.5 million light-years : 50 km/sec =
= (2,500,000 ∙ 365 ∙ 24 ∙ 60 ∙ 60 ∙ 300,000 km) : 50 km/sec
= 4.73 ∙ 1017 seconds


The molecular vibration period : the Local Group's vibration period =

   = 10-13 second : 4.73 ∙ 1017 seconds = 1 : 4.73 ∙ 1030


The Rule Of Equal Speed

In the universe of fractal structure, the speed of any corresponding motions between two adjacent levels of fractals must be unchangeable because time and space change in the same ratio.


(1) Stars in the galaxial system correspond to electrons (actually, to ultra-small particles in electrons).
Both are turning around each nucleus at 250 km/sec approximately.


(2) The galaxial nucleus corresponds to the atomic nucleus.
Quasars are known to be nuclei of furiously active galaxies.
Matter in quasars are observed as moving nearly at the velocity of light.


Similar motions are observed also in the atomic nucleus.
Nutrons are turning around inside the nucleus at the rate of 1022 times per second and the speed of such motion is faster than 30,000 km per second, i.e. a quasi-light speed.



In this essay I have demonstrated Fractal Cosmology using various data produced by modern science.

One point I feel wanting is that I have to use typical data, which inevitably leads to the adoption of a variation.


If scientists accept this new theory and sort out what particular celestial bodies correspond to what particular particles in the micro-world, exact comparisons will be possible without any variation.


Today mankind is pouring precious funds and time into the research of fundamental questions of the material world.

If scientists apply Fractal Cosmology to their research, they may be able to get answers for most questions, or obtain proper interpretations of various phenomena of the universe, by comparing the micro-world with the macro-world.


In the infinite universe, replications of fractal structure have neither a beginning nor an ending.

But there exist levels in the fractal universe, and, we understand now the magnifying power at each level is 1030.


Human science has progressed to the limits of their vision.

Fractal Cosmology may invite mankind into the world of infinity.


The End.

                                Written by Yun Pyo Jung

  (1)Encyclopaedia Britannica
  (2)Chronological Tables 1991,
     edited by National Astronomical Observatory of Japan
  (3)Barely Existing Things,
     written by J. W. Kim, Ph. D.

             *     *     *     *     *     *     *     *

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The book "Infinite Universe in a Mote" was published in 1994

from Sagyejul Publishing Co., one of the major publishing companies in Korea.

It has 290 pages.

It explains the Fractal Cosmology precisely in easy words.

Any publishers who want to publish this book in your language may write a letter to the author by E-mail :

This page ( is a copy from: , Yun Pyo Jung.

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