Saturday, March 30, 2019

Forest inhabitants

This is a translation of an old Russian story appeared in Russian Internet around 2000.

The Bear was an ugly, clumsy and dirty beast. However, there was no one kinder and nicer in the whole forest. But the animals notice only his appearance, and because of this, Bear felt terribly offended, caught them and brutally beat them with his feet. Therefore, the animals did not like him. Although, he was very kind and cheerful. He loved funny jokes. For these jokes, animals started to terribly hate him soon and beat him often. Yes, it's hard to be kind and cheerful in the world.

The Wolf was ugly and dirty too. And he was very evil and cruel. But the animals did not hate him and did not beat him. Because Wolf died in early childhood. Because the Bear was born before the Wolf. Yes, it is nice, when Good overcomes Evil.

The Hare was also evil and cruel. And dirty. And he was cowardly. The Hare has never done bad things to anyone. Because he was afraid. But he still had been severely beaten. Because Evil must always be punished.

And the Woodpecker was also evil and cruel. He did not beat the animals, because he had no hands. Therefore, he took out his anger in the trees. He was not beaten. Because they could not reach him. Once he was crushed to death by a fallen tree. It was rumored that it took revenge. After that, the animals were afraid for a month to pee on the trees. They peed on Hare. Hare caught a cold and died. It was clear to everyone that the Woodpecker was guilty of everything. But he was not touched. Because they could not pick him out from under the fallen tree. Yes, Evil sometimes goes unpunished.

The Mole was small and blind. He was not evil. He just did his job well. It was he who undercut a tree that fell on a Woodpecker. No one found out about this, and therefore he was not beaten. He was rarely beaten. More often frightened. But it was very difficult to frighten him because he was blind and did not see that he was frightened. When it was not possible to frighten Mole, the animals were very upset. And they beat the Bear. Because it was very disappointing. One day, the Bear also wanted to scare Mole. But Mole was not afraid. Because the Bear killed him. Unintentionally and accidentally. Just because Bear was very clumsy. And the animals beat him very badly. Even despite the fact that Bear said he was joking. It's bad when no one understands your jokes.

Fox was very sly and dodgy. She could easily trick anyone. When she succeeded, she was not beaten. But sometimes she was not lucky. And they beat her. All animals together beat her. And she could not trick anyone. Because it is very difficult to trick someone when they beat you. Once she was beaten to death. Yes, the truth always comes out.

The Boar was big, strong and scary. Everyone was very afraid of him. And therefore he was beaten only by all forest animals together. Or they simply threw stones at him. Boar did not like this very much. And one night he hid all the stones in the forest. For this, he was beaten very badly. Boar never hid stones again. Truly saying - time to gather stones together and time not to touch them ever.

The Rat was neither evil nor good. He was just a Rat. He often was ratting. And they were afraid to beat him. And everyone was tired of his ratting at some point. And then he was beaten to death. Because otherwise, he would have died of old age. Someday. When the Rat died, Bear cried heavily. Because he secretly loved the Rat. Yes, love is blind.

The Hedgehog was small and prickly. He prickled. He was not evil, he was prickled by nature. Because of this, he was beaten only in the stomach. Hedgehog did not like this and began to shave bald. And then they began to beat him like everyone else. Yes, it is very difficult to be different from others.

The Skunk was almost like the Hare. But only very smelly. He smelled bad. He was beaten only in a plastic bag. Then the smell was not so strong. Once Skunk had a birthday. He invited all the animals because he was greedy and loved gifts. And the animals gave him a new plastic bag. And they beat him badly until he lost consciousness. And Skunk choked in the plastic bag. So he was buried as is. In the plastic bag. In a Very Far Forest. Because the dead Skunk was stinking even more. Then came the inhabitants of the Very Far Forest and severely beat everyone. They did not like the smell of a dead Skunk. Yes, we must live in peace with our neighbors.

The Hamster was also very greedy. And rich. If he shared his wealth, he would not be beaten so much. But he was very greedy. For this, he was beaten hard. And he still had to share. And he cried bitterly. Yes, the rich are crying too.

The Lion was the king of beasts. He ruled the forest. Kings are not supposed to be beaten. This is the law. But the animals bump that law long time back. The animals beat the Lion too. For nothing. Because it has become a tradition here.

In case of repost, please keep link to this post.
Original Russian text can be found here.

Tuesday, August 14, 2018

How I built 3D version of fractal – Pythagoras Tree

Once I was reading in Wikipedia different mathematical articles and accidentally opened an article about Fractals and I liked the picture with 2D Pythagoras tree.


Then I wanted to see how it would look like in 3D and search returned me this:


As it is clearly seen, this one is 3D Model made in one of the 3D Editing software. Inspired by this picture I decided to build my own Pythagoras Tree from wooden coffee sticks.

So, I managed to make 3-level tree:
  • First level – One big cube (12 sticks)
  • Second Level – Four cubes which are 1.41 (square root of 2) times smaller (4*12=48 sticks)
  • Third level – 16 small cubes (16*12=192 sticks)
In total 252 sticks were required, which were connected by rubbers. And this is what I got in the end:



I took my time and spent 5 minutes per day, this is why the whole process took around 6 months.

After this, I made 270 photos from different sides and on 3 level. With special software, I managed to make 3D Model out of these 270 pictures. This is the model:

Video with an explanation of the creation process of Pythagoras Tree and result:

Как я делал трёхмерную версию фрактала – Дерево Пифагора

Как то раз я читал на википедии разные математичекие статьи и наткнулся на статью про фракталы, и там мне понравилась картинка с двухмерным деревом Пифагора.


Потом захотелось посмотреть, как бы это дерево выглядело в 3D. И поиск выдал такое:


Как видно это 3D модель, выполненная в каком-то 3Д редакторе. Воодушевившись этой картиной, я решил построить свое дерево Пифагора из деревянных палочек для кофе.

Итак, удалось сделать дерево из 3-х уровней:

  • Первый уровень – Один большой куб (12 палочек)
  • Второй уровень – Четыре куба в 1.41 (корень из 2) раз меньше  (4*12=48 палочек)
  • Третий уровень – 16 маленьких кубиков (16*12=192 палочки)

Всего потребовалось 252 палочки, которые скреплялись резинками для денег. И вот что получилось:



Делал потихоньку, по 5 минут в день, поэтому весь процесс занял примерно месяцев 6.

После этого я сделал около 270 фотографий с разных сторон и на 3-х уровнях. С помощью специального софта удалось построить 3D модель из этих 270 фотографий. Вот эта модель:

Видео с пояснением процесса создания Дерева Пифагора и результатом:

Monday, August 13, 2018

Забавные иконки ожидания/загрузки чего либо, основанные на научном подходе

Введение

Однажды я пытался найти веселые научные иконки ожидания или загрузки, но нашел всего несколько штук, типа вращающийся атом, молекула ДНК, вращающаяся земля и другие планеты. Но большинство из них были так сказать "плод воображения дизайнера" об научном объекте, а не результат реальных научных вычислений. Ниже представлены примеры стандартные иконки, которыми пользуются почти все:
      

После безуспешных попыток найти подобные иконки я решил сделать их самостоятельно основываясь на научном подходе и реальных научных вычислениях (или почти реальных:)). И вот что получилось.

Прецессия орбиты планеты в гравитационном поле звезды

Эти иконки были созданы с использованием одного из решений уравнений Эйнштейна из Общей Теории Относительности. Они описывают прецессию орбиты планеты и впервые это явление было открыто для орбиты Меркурия и объяснение феномена было одним из первых доказательств Общей Теории Относительности Эйнштейна. Полученные иконки показаны ниже. Используйте их где хотите :). Я подтверждаю, что они находятся в общественном достоянии с точки зрения авторских прав, т.к. они были созданы мной :)
Loading icon in black color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in blue color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in dark pink color based on Planet Orbit Precession calculated from Einstein General Relativity
Loading icon in green color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in pink color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in red color based on Planet Orbit Precession calculated from Einstein General Relativity
Loading icon in sea green dark color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in sea green light color based on Planet Orbit Precession calculated from Einstein General Relativity Loading icon in light blue color based on Planet Orbit Precession calculated from Einstein General Relativity

Фигуры Лиссажу

Фигуры Лиссажу больше математическая абстракция, но всё же часто встречается в физике, например, при исследовании и сравнении формы двух синусоидальных сигналов с помощью осциллографа. Как сейчас помню делали подобные лабораторные работы в универе :) Математически они похожи на окружность, но с различными фазами, частотами и амплитудами по осям X и Y. Как и предыдущие иконки, Я подтверждаю их принадлежность к общественному достоянию с точки зрения авторских прав, так что все могут их использовать :)

Waiting icon in black color based on Lissajous curve Waiting icon in blue color based on Lissajous curve Waiting icon in black/red/green/blue colors based on Lissajous curve
Waiting icon in dark pink color based on Lissajous curve Waiting icon in green color based on Lissajous curve Waiting icon in pink color based on Lissajous curve

Waiting icon in red color based on Lissajous curve Waiting icon in dark sea green color based on Lissajous curve Waiting icon in sea green color based on Lissajous curve

Waiting icon in light blue color based on Lissajous curve Waiting icon in rainbow colors based on Lissajous curve

Все вышеперечисленные иконки могут быть скачаны в одном zip архиве тут.