Naked Science Forum
On the Lighter Side => New Theories => Topic started by: Gerasimov on 17/09/2013 15:29:59
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Greetings, humans! I'm from Ukraine. My English is very bad. So I will use a Google Translate.
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 (http://xcont.com/pattern.html)
The algorithm is simple to indecency. Actually these things look like this:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Falg.jpg&hash=36c4af88bb7064c27db2ccf228c4eba9)
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:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpngs%2F23x13.gif&hash=939eae304fe12297a9ce65f9d606e562)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpngs%2Fgerasimov_carpet_23x13.png&hash=7cc6bf634d9c07527edfe94565efca34)
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).
Сlickable:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Fprch_tumb.png&hash=a251f2ad6037a1b0939d7a35302f9f7d) (http://xcont.com/pattern/prch.png)
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? "Пацан сказал - пацан сделал" (do not know how to translate it to English :).
Painted the largest enclosed area.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi1.png&hash=4caeb11f5d7410c2487f75f68cd30296)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi2.png&hash=ceafb6d75afd1412c3e3377671e36830)
233х144:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi3.png&hash=5a1ca6acf1ce06e30263bd586a31cd39)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi4.png&hash=9e824bbcb6e93ccc86bb553bfda87f47)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi5.png&hash=c772b6fd5e30a01069023125c8d104a4)
987х610 (pressed 5 times):
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Ffibonachi6.png&hash=29c18a07a091137587acea81475c1839)
233х144 и 987х610 - identical :)
As you can see, fractal repeats part of the overall fractal increased by (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpattern%2Fphi.png&hash=7c3264402ae2edf49945455ae1f0ddb1)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpngs%2Ffibonacci%2F223x144_2.png&hash=d5bc7c5d206c7e46873aef33f3801680)
Fractals, as they are.
Site: New kind of fractals - Fractals in relatively prime integers (coprime integers) (http://xcont.com/)
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?
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpattern%2F1377189269846_thumb.png&hash=8004be1ff981140103d49b5abee0cef9) (http://xcont.com/pattern/1377189269846.png)
Сlickable (enclosed area of fractals - "brain slugs"):
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fxcont.com%2Fpatterndxdy%2Fyzorchik_tumb.png&hash=beed6bd6983d929bd94cf2aa09009ea4) (http://xcont.com/pattern/yzorchik.png)