The Beauty of Prime Numbers
ฝัง
- เผยแพร่เมื่อ 15 ต.ค. 2022
- Immerse yourself in the Incredible and Wonderful World of the Beauty of Prime Numbers. This video is an author's exploration of prime numbers using knowledge of the Python language (Pygame, OpenGL)
Source Code (2d visualizations):
drive.google.com/file/d/1AfHV...
Source Code (3d visualizations):
drive.google.com/file/d/1pONB...
Video inspired by this article:
www.cantorsparadise.com/unexp...
#coderspace #primes #primenumbers
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I can't believe I only just found this channel, it's literally perfectly aligned with my interests. Great video!
ditto! Thanks for sharing.
0:40
The ending looks like the pipe screen savers of the 90s.
at first i thought the same 😅
@@CoderSpaceChannel There's something really familiar about the movement. Maybe they used primes to drive those pipes.
I think it's more based on randomness, with a check for a free direction of movement
1:30
1:30
6:02 So that's how grandma made those cool abstract patterns on the carpets. I also realized that you can check if your grandma is good at maths by the patterns of her carpets! That's just amazing! 👍😎
DAAAAAAAMN bro. DAMN. Not only did you create a really nice video (love how specific you were with how you implemented things), but that ending structure is fucking INSPIRED lol. Like... what does that shape look like once it is "finished" haha.... damn. So curious. It would be mind-blowing if it somehow returned to the start :P but that seems impossible. So many interesting mathematical implications from a generation like that; I hope someone dedicates more study to your creation!
I would love to see a continuation of that last test, where a function can detect if any cube (at all) overlaps with one another (by a %) and adds into a counter. Anyway, very interesting to see all the visualizations especially in 3D
Prime pipe maze?
Prime-steering-informed architecture?
Wonderful video. The Sierpinski triangles mind-blowing. Where did they come from?!
it is everywhere, I also generated this triangle with the chaos method, with the help of l-systems and now prime numbers
I'm currently binge watching all of your videos, love it!!
It took me a while, but the triangle fractal makes a lot of sense. When you bitwise OR your coordinates you will get repeating sections of odd numbers divided into chunks of powers of 2. What is interesting is that a large number of coordinates are prime numbers.
Found this channel and I want to say that it's amazing, truly fascinating world of visualizing math
It's amazing how well done this video is.
Great video, the script really showed your passion for this topic
"Prime Ladder" kinda pops into my head. Or, that scene on the rooftops in Mary Poppins where she forms the smoke into steps and they walk up... but in 3D 😁
Awesome skills. First thought that came to mind on your rendition was Labyrinth. It reminded me of the movie the Labyrinth with all the twisting pathways that lead in all directions.
Cool video and nice bg music :)
Truly a mentor.
thanks for the video, superb, watched the whole thing!
Very interesting take on prime numbers visualizations!
For some reason, this makes me feel insignificant.
So beautiful!
Amazing. Really enjoyed this one!
Love your work and presentation
Why is this so insanely good?
This is really awesome! I have made 2-d prime structures in the past also but never 3d.
This is amazing. Thank you for sharing!
That’s something I saved and I will be coming back to. So much hard work and great job done by you! Congratulations. I will be sharing this video to all my friends
Stunning stuff here...
for a beginner programmer and someone who used to hate maths this is just way beyond me.
*Some People:* There's no evidence of design in nature.
*Prime Numbers:*
Amazing videos indeed. You deserve milloins of subs :)
Amazing video!!!
This channel is going to get very big!
You 're expert in python. It's amazing..
Awesome video, This video inspired me to make my own engine and code conways game of life algo to visualize the mathematical models. I will try to play around with the rules and lets see what I witness.
Beautiful.
Fun fact: get rid of prime numbers and simply play with XOR and OR functions and you will see Sierpinsky triangles appear. In fact it appears in various places when you play with datas like in the "chaos game" or the blood rhesus table.
infinite amazement
Truly nice.
wooow glad i found my people in this comment section .. not everyone is this excited to watch such stuff
Very interesting
great stuff
Man this is so cool
best of best
Regarding the 3d random walk, does it intersect with itself?
Beautiful visualizations.
the final prime number structure you made reminds me of random walks
An easier way to tell if a natural number n is prime is to calculate ((n-1)!+1)/n. If the result is an integer, then n is prime (or 1). Otherwise, n is composite.
I have tested this and in terms of performance, using Wilson's theorem is a "less" efficient method for checking prime numbers (even if you cache the factorial values)
sounds incredibly inefficient for large n values
hi !! I love you're videos, I tried running the code but I keep getting the error
self.position = glm.vec3(position)
AttributeError: module 'glm' has no attribute 'vec3'
Do you know how to fix this?
You may have installed the wrong glm module. Check:
pip install PyGLM
I think you need to call the final render the Number Pipeline! An homage to the early screensaver
The hexagon spiral for primes uses this formula:
.75*x^2 + 1.5*x + 23 = mostly prime numbers when x is an even number.
Please more 3D number patterns !
Do the last one again. But instead have it go only right at the number in between twin primes. Then have it alternate from left to right at the number in between twin primes. Look at it then. I did this in on paper and it was pretty cool. Would like to see it in three 3d also at the number in between the twin primes.
I wanna do something like this in Unity 3d. How awesome would it be if the player had a say in how his path is unfolded.
there exists chains of consecutive numbers without prime numbers of arbietrary lengh. So the "prime laberynth" can have columns in one direction arbitraery large
A name for your block maze? How 'bout the endless Minecraft dungeon? It would need a world higher than 256 though haha
The 2d-version works perfectly
The 3d-version gives me only a black screen/black window. I think it relates to pygame. I can't find a solution. Do you have a suggestion?
Three letters: WOW🎉
im wondering if the final structure ever self-intersects
You ever see a new visualization following rules with basic maths and wonder if you're looking at the core logic of the universe unfold before you?
I truly believe that the universe is a holographic reflection of the matrix of mathematics :3
Also maybe 🤔 you could call it a Prime Snake or Snake-map or Snake trailing?
Why are you checking for prime number from 3 up untill square root of entered number? What's the math behind it?
If a number n is not a prime, it can be factored into two factors a and b:
n = a * b
Now a and b can't be both greater than the square root of n, since then the product a * b would be greater than sqrt(n) * sqrt(n) = n. So in any factorization of n, at least one of the factors must be smaller than the square root of n, and if we can't find any factors less than or equal to the square root, n must be a prime.
It's the _Prime snake_ 🐍 Btw., could it be possible to change the turn in accordance with the distance difference to the previous and next prime?
Prime pipes. Cuz that reminds me of a Windows screensaver
I saw a small man holding a gun in your wallpaper :D @07:01
I will pay money to have you work on a project with me. Been working with primes for years and need a visualization in both 2 and 3D
Do you plan to share code .. For educational purposes?
A link to the source code (for 2d) is available in the video description
ill call the number line a Prime Spagetti
I programmed in pascal and c/c++ but this programming language seems way complicated for me.
A serious question:
Does anyone know that there is a pattern in factorials of all N ? (N being all numbers inclusive of primes)
I have found it.
Anyone interested - let me know.
Prime track.
we have great ways to visualize prime numbers, but we still can't derive the formula for n primes
is 1 not considered prime?
What's the music name?
Traversing - Godmode
Call your discovery 'Bob'. It's short, a palindrome, and dyslexic friendly. 🤣😎
I am scared
????
Why robot voice :c other than that cool video
Prime Sierpenski Lattice
The end i think its should be prime line or line of the prime
Source code?
A link to the source code (for 2d) is available in the video description
@@CoderSpaceChannel Thanks! No source for 3d?
added, link available in description
rEvEnGe 0f Th3 N3RdZ
I bet u all took a few screenshots of these patterns
6:41 no we actually do live on a simulation due to me seeing some weird syit happening with balls
The proof is due to the balls NOT THE SIMULATION
pipes
make an infinite game based on it
Fun video, however, the patterns you see when you apply the xor and or operations has nothing to do with prime numbers. If you change your isPrime function to something completely different that will return true/false in a deterministic way, you will still see interesting patterns. To be sure, I tested this myself and even with a function as simple as isPrime(x) { return ((x % 14) == 0); }, I got complex structures, very similar to what you got using prime numbers.
Great experiments, very interesting and informative.
Though, if I could make a suggestion? Just get a mic and record your real voice bro, I can't stand that AI generated robo voice in this. It's not convincing in the slightest, no emotional infliction, dehumanized quantization in the timing. Nobody annunciates words that precise, but I'll admit AI voices are indeed improving.
Let's start learn Math 👽
First
what
You should consider applying these voxel renderings to a cube of rgb color space en.wikipedia.org/wiki/RGB_color_model#Geometric_representation keep up the awesome work