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.
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
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.
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
"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 😁
That's pretty cool! I wonder what it would look like to use randomly selected odd numbers instead of primes - Would you still get the fractal triangles and other patterns?
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.
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.
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?
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)
there exists chains of consecutive numbers without prime numbers of arbietrary lengh. So the "prime laberynth" can have columns in one direction arbitraery large
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.
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?
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.
When I run the code: line 25, in fillSide self.arr[self.pos[1], self.pos[0]] = [255] * 3 if isPrime(self.num) else [0] * 3 ~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^ IndexError: index 1001 is out of bounds for axis 1 with size 1001 Please help me!
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?
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.
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.
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.
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
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
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.
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! 👍😎
I'm currently binge watching all of your videos, love it!!
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
The hexagon spiral for primes uses this formula:
.75*x^2 + 1.5*x + 23 = mostly prime numbers when x is an even number.
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
Truly a mentor.
thanks for the video, superb, watched the whole thing!
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
The primes video is mesmerizing, 0:06 reminds me of my grandma embroidered dress even the same organized colors ,l swear ,it’s embroidery art 😅😂❤
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
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 😁
Stunning stuff here...
for a beginner programmer and someone who used to hate maths this is just way beyond me.
That's pretty cool! I wonder what it would look like to use randomly selected odd numbers instead of primes - Would you still get the fractal triangles and other patterns?
I'm also really interested in this
Very interesting take on prime numbers visualizations!
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.
So beautiful!
It's amazing how well done this video is.
This channel is going to get very big!
This is amaze, and it is awesome/amazing. It is beautiful and incredible, and it is amazing.
Amazing videos indeed. You deserve milloins of subs :)
This is really awesome! I have made 2-d prime structures in the past also but never 3d.
Cool video and nice bg music :)
Love your work and presentation
*Some People:* There's no evidence of design in nature.
*Prime Numbers:*
Thats just amazing 😍😍😍
Regarding the 3d random walk, does it intersect with itself?
Beautiful visualizations.
Why is this so insanely good?
This is amazing. Thank you for sharing!
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.
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
Amazing. Really enjoyed this one!
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
there exists chains of consecutive numbers without prime numbers of arbietrary lengh. So the "prime laberynth" can have columns in one direction arbitraery large
I think you need to call the final render the Number Pipeline! An homage to the early screensaver
You 're expert in python. It's amazing..
wooow glad i found my people in this comment section .. not everyone is this excited to watch such stuff
Amazing video!!!
A name for your block maze? How 'bout the endless Minecraft dungeon? It would need a world higher than 256 though haha
the final prime number structure you made reminds me of random walks
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.
10:47 the mapping can be called the prime elevator
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?
ill call the number line a Prime Spagetti
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.
im wondering if the final structure ever self-intersects
This is very interesting
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?
infinite amazement
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.
Call your discovery 'Bob'. It's short, a palindrome, and dyslexic friendly. 🤣😎
Challenge: convert these prime number graphics ito a Minecraft map.
Do you plan to share code .. For educational purposes?
A link to the source code (for 2d) is available in the video description
Please more 3D number patterns !
Beautiful.
Man this is so cool
When I run the code:
line 25, in fillSide
self.arr[self.pos[1], self.pos[0]] = [255] * 3 if isPrime(self.num) else [0] * 3
~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^
IndexError: index 1001 is out of bounds for axis 1 with size 1001
Please help me!
Very interesting
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?
great stuff
best of best
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.
I programmed in pascal and c/c++ but this programming language seems way complicated for me.
Truly nice.
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
Prime pipes. Cuz that reminds me of a Windows screensaver
Three letters: WOW🎉
we have great ways to visualize prime numbers, but we still can't derive the formula for n primes
I saw a small man holding a gun in your wallpaper :D @07:01
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.
What's the music name?
Traversing - Godmode
The end i think its should be prime line or line of the prime
is 1 not considered prime?
I think it's useful for one to not be considered prime
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.
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
For some reason, this makes me feel insignificant.
name for map of numbers: Prime Chart,
Why robot voice :c other than that cool video
i love you
I bet u all took a few screenshots of these patterns
rEvEnGe 0f Th3 N3RdZ
Polyspace I should say
I am scared
Prime Sierpenski Lattice
make an infinite game based on it
Prime track.
Let's start learn Math 👽
pipes
First
what
Urgh AI voices..... I would take any broken english over this mess...
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