This is the story of a star called Hoggar, searching for a magical object, the Shell of Wisdom, which is believed to make you wiser. All figures in the story are accompanied by Python scripts.
A very curious star called Hoggar, living in the Taurus Constellation, had heard that on planet Earth there was an island that hid a very special shell: the Shell of Wisdom. It was believed that anyone who found this shell, became wiser.
For this reason, he decided to land on the Island of the Shell of Wisdom searching for the treasure which would make him one of the wisest stars in the skies.
A figure of a five-pointed star which in our story represents the main character, Star Hoggar. Here you can learn how to generate such a figure using Python.
After he landed, Hoggar felt confused because he didn't know where to start searching for the Shell of Wisdom. Nearby, there was a forest with no trails or indications where to start looking. Anyway, he had to be brave and try something. So he approached the dense forest. He had only made few steps inside the forest when he saw a strange creature. It was a weird kind of butterfly, with very large wings and no head. At first, Hoggar was reluctant about approaching the creature, but then he found the courage to talk to it. Maybe it could help him.
-Hello, my name is Star Hoggar. I come from the Taurus Constellation and I am here to find the Shell of Wisdom, - he introduced himself to the butterfly.
-Hello Hoggar. My name is Harmonie, I am a butterfly with large wings that I use in order to fly, absorb the sunlight and sense the objects around me. I have no head because, well, I don't really need it. I do everything through my large wings.
Butterfly Harmonie in our story is designed as a harmonograph.
Hoggar was surprised. Apparently on the island there lived pretty unusual creatures.
Harmonie continued, slapping her wings faster as she talked:
-I am afraid you are going in the wrong direction. There is a friendly creature in the forest that helps every traveler who is sincere about finding the Shell of Wisdom. The name of this creature is "the Friendly Tree". Let's meet it so it can help you. Follow me!
Hoggar and Harmonie walked together in order to meet the mysterious tree. Hoggar was looking all around but couldn't see any special or magic tree. They all looked the same, static and normal. But butterfly Harmonie advised him that in order to find such special friends, as the Friendly Tree, one shouldn't look where one always has and it is essential to keep an open mind in order to be able to recognize someone with unusual and unique features.
Suddenly, they saw something weird in the forest. A short wooden trunk with no branches or leaves was standing in front of them. Hoggar was confused. Was that the Friendly Tree? It didn't look like a tree at all!
-You look surprised, - Harmonie giggled, - Yes, this is the Friendly Tree. Why don't you try waving at it and saying hello?
Hoggar approached the Friendly Tree and waved at it. Suddenly, the tree opened its magnificent branches to wave back at the visitor. Hoggar was amused looking at the sudden transformation of the tree.
A dynamic fractal tree, which in our story is called the Friendly Tree because it waves back at visitors and helps anyone who wants to find the Shell of Wisdom.
- Hello! Those are some very beautiful branches you have! - Hoggar complimented the tree.
- Thank you, friend, - the Friendly Tree answered, - How can I help you?
- I am looking for the Shell of Wisdom. Can you help me find it? - Hoggar said.
- I can give you some useful information, of course, but you are the only one who can find it. The Shell of Wisdom is located on the other side of the island. You have to walk through the forest, in that direction, and follow the rocks which have a circle engraved on them - the tree pointed one of its branches at a circle engraved on a piece of rock a few meters behind. -Then you will come across a cave. You can enter it only after completing a challenge. After you exit it you will be very close to the shell. And remember, should you encounter any form of rare beauty on your way, make sure to preserve it. I see you are quite determined and honest about collecting this shell. I think you will be one of the wisest stars in the sky soon.
Although a bit puzzled, Hoggar smiled, thanked the tree, and continued his journey. However, just as he was passing next to the tree he stepped over some roots, fell on the ground, and crushed his head. Now he didn't see just one circle on the rock, but many of them.
There was only 1 circle engraved on the rock, but Hoggar hurt his head on the ground and saw many of them.
- Careful, - the Friendly Tree said, - it's very nice to dream, but one should watch their steps time after time, don't you think?
After he took this wise advice, Hoggar continued walking with his friend Harmonie in the direction that the tree had pointed.
They had walked for about half an hour, chasing after the rocks with engraved circles, when a cave appeared in front of them. There was no other way to proceed since the cave was surrounded by very dense trees and bushes on the left, and a deep river on the right. They had to enter the cave, but there was a problem: the entrance was blocked by a big wall that they couldn't move. On the wall, there was a window. Suddenly, a writing appeared on the wall:
"All visitors must introduce themselves". An engraved arrow pointed at a bag of colorful laces of fixed lengths and a tape nearby. The writing disappeared again.
Hoggar remained quite confused.
-So, in order to be able to enter the cave, we need to introduce ourselves somehow using the laces and the tape. How do we do that? Introduce myself, hmm. Should I find a way to write my name on that window on the wall?
-Probably, - Harmonie replied, - but don't you think the window is a bit too small for that?
-Maybe I could try creating the initial of my name, - Hoggar suggested.
He took a few laces, tied them together to form the letter "H" and put them on the window using the tape. The letter occupied the whole area of the window. But nothing happened. The entrance remained blocked. Then the hint reappeared on the wall:
"ALL visitors must introduce themselves".
-Oh, we both need to enter our initials, - said Hoggar, - But how do we do that? The window is just too small.
-Maybe you should proceed alone, then, - Harmonie suggested, - After all, this is your journey.
-No way, - Hoggar objected, - you are my friend and I will not leave you behind. We will do this journey together. I just have to figure out a way to solve this puzzle. Let me think. So, we need to place both our initials on that small window. Actually, I don't have to place them next to each other, I could just place them on top of each other. I just need to create another letter "H" for your name, Harmonie and put it on my letter using the laces and the tape.
Hoggar took some laces of a different color, created another letter just as he had done few minutes ago, and put it on top of his letter, on the window.
The initials of Hoggar and Harmonie realized through matrix rotation.
Suddenly, the wall shifted to the right, allowing the two travelers to enter the cave. They went in together, and after stepping inside the cave the wall went back to its position blocking the entrance again. Since Hoggar was a star, he made enough light for both of them to walk through the cave and find the exit. After walking for about half an hour, they finally exited the cave. They found themselves near the seashore, where they could hear the sound of the sea waves.
-I think we reached the other side of the Island, - Harmonie said, - The Shell of Wisdom shouldn't be too far.
They walked towards the seashore and were amused by the sight of a wonderful piece of art lying on the ground. They remained speechless by its splendid colors and shapes.
An example of a Julia set.
The beautiful piece of art lying on the ground as a Julia set. Its colors were shinny, its patterns looked like flowers and islands. They just couldn't stop admiring it. Suddenly, it became dark. The weather became cold and the sky cloudy. It looked as if a storm was about to start. Hoggar began to worry.
- What's going on? - he asked Harmonie.
- I think a snowstorm is about to start, - she answered, - Maybe we should find a shelter.
- Yeah, we probably should, - Hoggar said, - Wait a minute. Remember what the Friendly Tree said? It said that we need to preserve any form of beauty we encounter on our way. At first, it didn't make sense to me, but now I get it. We need to preserve the Julia set from the snowflakes, which might damage its colors.
At that moment, the first snowflakes started falling from the sky. They had different shapes, some of them were quite simple, resembling triangles, others were more complex.
A level 7 snowflake.
Hoggar had to find a way to cover the Julia set from the snowflakes, otherwise it would get destroyed. The question was how? He had no umbrella, no cover, he couldn't move the Julia set to a safer place, its area was too big so he couldn't cover it with his own body. He couldn't find a way out. Harmonie didn't have any clue either, she was just slapping her wings, looking around for an object that they could use to cover the piece of art.
Hoggar observed her wings, they were quite large, but they could only be useful if Harmonie kept them horizontally. Furthermore, Harmonie couldn't move fast enough to cover all of the Julia set from the snowflakes. But Hoggar could! After all, this is what stars do, they shine bright and spin around incredibly fast. Maybe he could lie on the ground, keep Harmonie on his body, she would slap her large wings in order to keep the snowflakes away from the Julia set, meanwhile, Hoggar would spin all over the piece of art to protect the whole area.
-Harmonie, it's time to do some teamwork! - Hoggar explained the plan to Harmonie. She found the plan genius and agreed to give it a try.
And this is what they did. Hoggar lied on the Julia set and spun around keeping Harmonie on his body. Harmonie slapped her wings to keep the snowflakes away from the Julia set. The storm only lasted a few minutes and they managed to keep the painting untouched and dry. When the storm was over, they stood up and felt quite relieved that they managed to succeed in this task. However, they couldn't see the Shell of Wisdom anywhere. Hoggar looked around on the seashore, where they usually appear, but couldn't see it. He began to worry, maybe he had failed in one of his tasks and he didn't deserve to collect the Shell?
Suddenly, Harmonie called him:
-Hoggar, I think you are looking in the wrong direction. Have a look at the Julia set again.
Hoggar turned his head to the Julia set and was astonished by the image that he saw.
A star spiral, created by the rotation of a five-pointed star.
While he was spinning around to protect the painting from the snow, Hoggar created this large spiral trail that looked very much like a shell. It was very beautiful and unique. He didn't know he could do something like that.
-Do you understand what just happened? - Harmonie asked him, - You just created the Shell of Wisdom. Wisdom is not something that you find in some magical object, instead, it's something that you create, something that you learn with time. It's not hidden out there, it's born and nurtured inside of you.
-But how is that possible? - Hoggar wasn't convinced yet.
-Remember all of the wise things you learned on this island. You learned to ask for help, you learned to take a piece of advice, you proved yourself a good friend when you refused to leave me behind in the cave. You found creative solutions to your problems more than once. Through your experiences, you created your own Shell of Wisdom. Now I think you have become one of the wisest stars in the sky.
Hoggar smiled happily and felt proud of his journey, of all the new things he had learned. He knew this was just the beginning and had so much more to learn. He thanked his friend for her help and her nice words. They had a last walk together, hugged each other, and promised to meet again. Then Hoggar left the island and flew back home, to the Taurus Constellation.
Reference: Math adventures with Python (Peter Farrell)
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