All matter - is light.

[Gerasimov]

Greetings, humans! I'm from Ukraine. My English is very bad. So I will use a Google Translate.  :Hangman:
In 2002, I came up with an interesting piece. I was only 14 years old. I was thinking about fractals and chaos theory, and did not want to learn. Did not want to learn, and were forced to walk to school. I came up with a way to kill time on the boring lessons in history, geography, and other humanities. I'll try to explain in detail. All we need - a piece of paper into a cell and an ordinary pencil. If a piece of paper is not available and also no pencil - an online version of JavaScript: http://xcont.com/pattern.html

The algorithm is simple to indecency. Actually these things look like this:



Select the rectangle and let in the corner of the "quantum beam" (as I called it in 2002) The beam reflected from the walls and is lost at the other corner.

GIF:




If certain conditions were met - it turns fractal pattern.
If the conditions are not met (for example the obvious - the rectangle are equal) - pattern is not obtained. Of the less obvious example - the same pattern as it is impossible, if the size of the parties have a common divisor. In fact, the patterns are obtained only if the dimensions of both sides - are relatively prime (have no common divisor).

?lickable:



In the picture all the numbers from 1 to 30.

And now a little about Fibonacci and fractals.

Patterns represent a fractal.

What determines the pattern?

So you need to make a difference, too, was a prime number (the largest), its difference with the numbers, too, was simple and small, and so on, then there will be something interesting.

That suggests to us - what if you try to Fibonacci numbers? "????? ?????? - ????? ??????" (do not know how to translate it to English :).


Painted the largest enclosed area.





233?144:






987?610 (pressed 5 times):


233?144 ? 987?610 - identical :)

As you can see, fractal repeats part of the overall fractal increased by


Fractals, as they are.

Site: New kind of fractals - Fractals in relatively prime integers (coprime integers)

P.S.

And a little bit schizophrenic 11-year-old:

Then, thinking about the relations of chaos and order where chaos is taken in order, and in order - chaos. So that was then thought that when everything exploded (big bang, which I firmly believe), was a ray of electromagnetic energy that is in the early running in a small space (which is further expanded.) Since electromagnetic waves can be in the form of photons - this beam is uninterrupted. Where we see the intersection of electromagnetic waves - there appears the "matter" (https://en.wikipedia.org/wiki/Pair_production) in the form of fractal patterns. Thus is born the order out of chaos.

(2) there is no space in the quantum distance - so there is no common divisor. Always work pattern (what we call matter).
(1) The universe is expanding continuously and smoothly. A fractal is continuous (and also smoothly) goes from one to the other - what we call the motion of matter.
(3). The universe is not two-dimensional and three-dimensional (and from the point of view of the General Theory of Relativity - four-dimensional).
So fractals are much more difficult.

Perhaps the chaos - it is also a fractal?


?lickable (enclosed area of fractals - "brain slugs"):

[PickelledEggs]

Welcome. I wasn't expecting a math lesson today.

[Gerasimov]

Welcome. I wasn't expecting a math lesson today.

:))

[LikelyToBreak]

Welcome!  You seem to have thought about this quite a lot.  :-k

[Mister Agenda]

Sorry, I'm not qualified to critique that. Pretty, though.

[Gerasimov]

Sorry, I'm not qualified to critique that. Pretty, though.

In short:
At first, the big bang.
As a result of the big bang - a lot of electromagnetic waves (light) of different frequencies and in different directions.
As we know, the electromagnetic waves - oscillations of the magnetic and electric field.
At the intersections of these oscillations (where the vector coincided) - there are fractals. Many different fractals.
The space is growing - fractals also gradually changing.

[Gerasimov]

online version of JavaScript: http://xcont.com/pattern.html

[Solitary]

Fascinating! All growth in nature involves the Fibonacci numbers: 1 1 2 3 5 8 13 21 34 55 89  8-)  Solitary

[Jason78]

I like fractals! :D

[NeoLogic26]

I was told there would be no math.

Welcome, Gerasimov. Is your name a combination of something and a reference to Isaac Asimov?

[Gerasimov]

Is your name a combination of something and a reference to Isaac Asimov?

No. "ov" - is the suffix. Half of Russian names end with "ov". For example: Asimov, Gerasimov, Makarov, Kalashnikov, Vavilov, Pavlov...

[the_antithesis]

So you're Russian.

What's the hurry?

[Gerasimov]

So you're Russian.

What's the hurry?

No, I'm from Ukraine. Father - Russian, mother - Ukrainian.

[Colanth]

Welcome to the forum.

Calling a Ukrainian Russian is like calling an atheist a Catholic.  In English, Gerasimov, we say, "them's fighting words". :)  (I'm Ukrainian on my my mother's side.)

We have a few members who are very good at theoretical math.  We'll have to wait for them to comment.  I know enough to know that I'd have to study your posts quite seriously to understand what you're saying, and since it's getting late in the afternoon, I'm too tired.

[Jutter]

Interresting results. That doesn't mean I feel qualified to agree/disagree with the conclusions you draw from them.