Video není dostupné.
Omlouváme se.
Chaos game - Sierpinski triangle
Vložit
- čas přidán 3. 09. 2022
- This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: • Six Sierpiński Triangl...
In this short, we play the chaos game using randomness to find order and create the Sierpinski triangle. Can you explain why this works?
#math #manim #fractal #fractal #sierpinski #chaosgame #chaos #mathshort #visualmath
_____________________
Music in this short (a 10 second cut):
When The Lights Go On by Vlad Gluschenko | / vgl9
Music promoted by www.free-stock...
Creative Commons Attribution 3.0 Unported License
creativecommon...
long form video: czcams.com/video/IZHiBJGcrqI/video.html
damn you youtube for unlinking links
CZcams unlinking all links😢
😢
I’ve always wondered what happens if you start in the middle, pretty cool though
You have to throw away the first few dots to get a perfect picture. Still gives the same limiting behavior :)
Ah, I was also thinking that. Pretty cool!
That is the origin point of chaos.
I wonder what would happen if this was done with a circle using phi instead of ½?
I love fractals! It's like an infinitely looped video. This is a really cool way to create one!
This is such a beautiful result. 💙
Definitely so cool :)
you can also just get rid of the middle section for each iteration
Wooo Legends of Zelda
Sierpinski triangle jumpscare
My kind of thing.
Triforce
That is one of the weirdest mathematical things
🙂👍
Its... Its... A MASTERPIECE!! But when i flip it upside down it kinda looks like your you tube logo so that means your logo is made buy the sierpinski triangle
beautiful
Thank you! 😊
Interesting shape..
not really chaotic if the rule is very restrictive,1 the area is inside the triangle so it's not really random, 2 it's always half the distance of the dots inside of same triangle, you're bound to get triangle patterns eventually
Your random selection is the same
respective sequence used in the square
example.
Why can placing dots in a triangle yield the Zelda logo?
Can we animate long division in Manim ? If we could do you know any tutorial or document for the same ?
I would guess it can be done... but I can't think about how best to do it programmatically. I haven't seen it done.
@@MathVisualProofs How did you exactly learned manim ? Is there any path I could follow ? any definite tutorial from beginner to advance ? any ultimate documents ? could you teach me. I really really want to learn this software.
@@randomsircle I just got into it and starting playing around. Check out resources on the manim site, and maybe check out tutorials by @benjaminhackl . Those seem to be good ways to learn?
@@MathVisualProofs Thanks for help
i REALLY want to make this in Desmos...
What happens if you pick a point that's not the middle?
That was fantastic, but why??
can you proof this?
you can definitely prove it. But most likely not in a short :)
I did a Computer Science project at age 17, for which I chose to do fractal generation.
I looked at the generalisations of this method (and of taking Pascal's Triangle modulo 2), and discovered that if you start with a hexagon, and use ⅔ rather than ½, you get a fractal made up of the Koch Snowflake fractal, and if you start with a 3x3 square lattice of points with the middle one removed, and also use ⅔, you then get the Sierpinski Carpet
Edit: Just found your video about the hexagon case.
I have a video of the hexagon version you describe :) Very cool. Definitely a fun project to explore on one's one :)
thanks, today I did it on fortran and gnuplot 🤷🏻♂️
What if you also allow the midpoints of the edges of the triangle? What do you get then?
What if your first dot is in the center of the triangle
It's the limiting shape that looks like this. So you can throw away any number of initial points if you need. :)
What if we place points outside the triangle?
Limiting shape still the same. You won’t get any aggregation by that single point and you can’t see single points (here I have exaggerated points so you would see one or two rogue points). But this is more about long term behavior
Lets play the chaos game.
If your health drops to 0, you will lose
Chaos is order?
zelda shape
Does it also draw the original triangle's edges? Can't find a video that doesn't show the border but I have to know: how can a point ever appear along the original edges?!
You are right that the edges won’t be drawn. But the limiting shape will include points so close to the boundary that you would “see” the border triangle even though it is not in the set of points (the border points are limit points)
@@MathVisualProofs Super helpful. I saw a video on IG and I though my brain was going to explode trying to understand how the edge lines could be drawn precisely.
What happens if you start at the centroid of the equilateral triangle?
Der. Dumb question in hindsight.
Unless the first two iterations were the same vertex - which could happen.
Build A Triangle Of Sierpinaki
A Weird Dots
stock markets are fractals. wow.
Look at all that dark matter!
do it using the farthest vertex
Description is empty?
Hmm. Not for me. Check again maybe?
@@MathVisualProofs viewing the description on desktop in browser, I see the content, but not through the iOS application (maybe because out of date? But I’ve seen other descriptions on shorts with it, so that seems odd..?)
@@drdca8263 Yes. I have heard it happen before. Not sure why. I hope they fix it I guess. Thanks!
You have the rules wrong. If i put the first dot in yhe middle, this destroys this description
I say the limiting shape is the fractal. So where you start doesn’t matter because you are really looking for end behavior.
The Final Shape,
The Flawless Shape,
Divinity,
Harmony,
Prosperity,
Majesty,
The All-Shape,
The Law of 3,
Knowledge Given Form,
Breath of Formity,
The Trigonometress’s Purity,
The Edge of Unity.
Many names, the Azzeri call this divine shape, but simply refered to as:
The Triagon.
Why is the music volume 10 times louder than the speaking volume. Jesus, it's awful.
Yeah. Sorry. This one older than others. I am a bit better at sound editing now (though still not great)
30000 times is too much
not enough actually :)
This cannot be true
But you're watching it happen...
I’m watching an explanation which can be disputed. So, extrapolate for a sec and overlay the end pattern at the beginning of the process to reverse engineer it. For the sake of communication we will call a coloured in triangle a positive and the others negative. It has been put forward that the initial point is random. “But” there is only a 50% chance that that point is on positive triangle. And therefore each half point will be where? Not on its correct colour I think. Either A. It is wrong or B. It is actually possible to produce a negative of the pattern dependent on the initial point. If it’s B. I’ll reneg my dispute as mute.
@@MathVisualProofs oh and, as someone else has commented… you can’t just throw away the first few dots. That means it’s a wrong statement.
@@timmo971 the precise statement is that the limiting set is the Sierpinski triangle no matter what point you start with. So you can throw away any finite set of initial points.
Fake. trying for myself didn't work
Try again.
I did this today as well on my channel using MATLAB. Chaos Game!!
Very cool!