Map of Natural Numbers in 3D

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Map of Natural Numbers in 3D

Рет қаралды 9,316

Күн бұрын

Generating a Map of Natural Numbers and its 3D Renderer using the UMAP dimensionality reduction algorithm in Python and OpenGL.
Inspired by:
johnhw.github....
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Source Code:
github.com/Sta...
#coderspace #umap #opengl #python

Пікірлер: 65

@InfiniteCoder01 9 ай бұрын

I wonder, what it will look like if the colors would be represented as three more domensions

@OpenGL4ever 5 ай бұрын

I wonder, what it will look like if you make it four dimensions and using time animation as fourth dimension.

@cristianocenta2624 4 ай бұрын

This is incredible... I was exploring the possibility of numbers being "beings", with specific characteristics that make them cluster accordingly - there can be a relation between them that we cannot perceive with our 2D chalk-wall... This is what I was looking for. So glad I found this video! Really amazing job, man.......

@DBo-iv9qv 8 ай бұрын

That's cool I'm wondering why odd and even numbers draw these closed figures, and why even numbers tend to look circular more than the odds

@OpenGL4ever 5 ай бұрын

I would like to know that, too.

@kellymoses8566 21 күн бұрын

Man this is some excellent brain candy. Feels like it could be in a Greg Egan novel.

@azaias 9 ай бұрын

Wow! These visuals are pretty inspiring!

@jeffcummings3842 9 ай бұрын

your videos never cease to amaze and inspire, thank you for creating and sharing!

@simondev758 9 ай бұрын

This is crazy cool

@looking8994 8 ай бұрын

Bravo, standalone coder

@pmlbeirao 8 ай бұрын

This is one of the coolest things I've ever seen.

@alexandrepv 8 ай бұрын

This is so cool :) Could you elaborate more on UBOs and SSBO's? I've been trying to improve performance in my own code and they seem to be good candidate solutions. Please, keep these videos coming mate! You are combining the accessability of Python with the power of 3D graphics in a way not many, if any, have done before on KZfaq. A new generation of graphics and ML enthusiasts will come from this channel alone :D

@elorating 9 ай бұрын

This is some great great work. Bravo!

@griffinschreiber6867 8 ай бұрын

What a time to be alive!

@anon_y_mousse 9 ай бұрын

Beautiful visualization. I wonder what it would look like if you took the 6th dimension data and represented the last three components as color values.

@mrdixioner 3 ай бұрын

Красота математики!!!

@kimeg7294 9 ай бұрын

The primes are just leftovers. You cannot pinpoint a specific prime number (too large to be discovered yet) without getting there by basic iterative steps. We can only guess roughly how many primes are in a certain interval of natural numbers.

@kellymoses8566 21 күн бұрын

UMAP is an absolutely amazing algorithm. The math behind it is just so very hard. tSNE is much easier to understand.

@alvarocubi 9 ай бұрын

You are a genius, thanks for sharing your beautiful creation

@dclxviclan 9 ай бұрын

Cool visualization ❤

@BORCHLEO 6 ай бұрын

this is just amazing. so beautiful and so intelligent.

@BORCHLEO 6 ай бұрын

check out my new video on my paper which presents the sieve of eratosthenes in the complex plane if you want to see some insanely new prime functions: kzfaq.info/get/bejne/n9l5papozZ-qias.html

@nycoshouse 2 ай бұрын

you have to add a crosshair and display number under it in a corner of the screen with properties (prime divisors)

@eternal_learner9943 9 ай бұрын

Geometry = Numbers in space.

@OudinAlex 9 ай бұрын

Simply stunning!

@erc0re526 9 ай бұрын

Awesome! your stuff is always interesting. Seeing this in 4D would be fascinating... 3D slices of this little cosmos... (Have you changed your IDE theme? What is this one? It's gorgeous!) Edit: also I noticed, I'm curious about the reason for your trailing underscore naming convention!

@CoderSpaceChannel 9 ай бұрын

Thanks. The IDE theme is the same, except I changed a few colors slightly to suit me. I use underscore just to make the names of the arguments different from the outer scope names

@erc0re526 9 ай бұрын

@@CoderSpaceChannel ahh I see! Thanks

@olbluelips 7 ай бұрын

Honestly inspiring, I love it! Also, why not reduce to 6 dimensions and have the additional 3 map onto HSV? A 7th dimension could be used to make an animation over time. I bet there would be some interesting structure there

@andrzejsiebieranski7239 9 ай бұрын

Good Job Stanislav !

@iamdigory 6 ай бұрын

Please tell us more about which numbers end up in which structures and why

@VCC1316 9 ай бұрын

First of all, hats off. This is just brilliant! Secondly, I am wondering ... UMAP can be run in supervised mode. That means that you could label e.g. the prime numbers as '0', and the rest as '1'. Assuming prime numbers will cluster efficiently, then, you could see if projecting a new test point (number) in the map, and see where it falls (in the primes cluster or elsewhere?). What I want to get is: can this be used to easily find prime numbers? Because that would be HUGE.

@CoderSpaceChannel 9 ай бұрын

UMAP has many settings, but they all seem to be related only to dimensionality reduction. But I like your idea! By the way, there is a UMAP implementation for the GPU available in the NVIDIA RAPIDS cuML library, maybe there is something interesting there.

@VCC1316 9 ай бұрын

@@CoderSpaceChannel After thinking more on my own statement, the only drawback would be to represent the numbers in an other way other than factorizing on prime numbers, or else prime number discovery is by default impossible. But I assume one could just perform any other compact factorization, e.g. representation on base 16, or even more. I may try this as soon as I have some spare time ....

@VCC1316 9 ай бұрын

@@CoderSpaceChannel I started playing with the idea, using PCA instead of UMAP (and a not optimized code such as yours)... Is there any way I can send you the jupyter notebook? Like, a mail contact via this channel or ... Not pushing man, only if you have time!

@pr4shantishere 7 ай бұрын

Hey, can you do a tutorial on physics with opengl and python

@Sourcecodemastergoaheadcheater 6 ай бұрын

You know what father likes too see. Cool interesting and puzzling things 😂😂 ty babies

@silloo2072 7 ай бұрын

We need more videos

@FunnyChannel-zp9ov 8 ай бұрын

please create a ultimate ursina tutorial and thank you for this video

@minecraftermad 9 ай бұрын

I wonder what tranformations you'd need to align this with the n dimensional model that natural language forms?

@rezashir3873 9 ай бұрын

you are the best. keep going

@pasindu1996 7 ай бұрын

Its amazing

@ek_minute_ 5 ай бұрын

why don't you have millions of subs???????

@eternal_learner9943 9 ай бұрын

Beautiful.

@TheCptEd 9 ай бұрын

So good!

$@fancyfractals2820$

@fancyfractals2820 9 ай бұрын

Awesome!

@KarolWasiluk 7 ай бұрын

Can you write a Might and Magic 6 Mandate of Heaven style game in Python? Idea for the project in the next video :)

@kellymoses8566 21 күн бұрын

I wonder if this could be done with functions somehow.

@HoSza1 9 ай бұрын

Why isn't multiplicity accounted for? The vector of 12 should be 2, 1, 0, ... instead of 1, 1, ... because 12 = 2² * 3¹.

@Pythonister695 9 ай бұрын

amazing

@Clepy 8 ай бұрын

CAn u teach us how to make a cool fps game like with good graphics and u deserve a sub

@michaelkewl7056 9 ай бұрын

Awesome

@shick1 9 ай бұрын

Не, натуральные числа это деревья (графы), где листья это простые числа, например 2*3^(5*11)*5*7 =) круто было б такую если визуализацию кто-то сделал... Точнее все узлы - простые числа

@MaxCarponera 9 ай бұрын

pygame 2.5.2 (SDL 2.28.2, Python 3.10.12) -> WIN_RES = glm.ivec2(1280, 720) AttributeError: module 'glm' has no attribute 'ivec2'

@CoderSpaceChannel 9 ай бұрын

reinstall PyGLM

@MaxCarponera 9 ай бұрын

@@CoderSpaceChannel pip install --force-reinstall --no-cache-dir umap-learn scipy pygame moderngl PyGLM [...] Successfully installed PyGLM-2.7.1 glcontext-2.5.0 joblib-1.3.2 llvmlite-0.41.1 moderngl-5.8.2 numba-0.58.1 numpy-1.26.1 pygame-2.5.2 pynndescent-0.5.10 scikit-learn-1.3.2 scipy-1.11.3 tbb-2021.10.0 threadpoolctl-3.2.0 tqdm-4.66.1 umap-learn-0.5.4 Sorry. No avail, same error. Ubuntu 22.04.1 😕 Your other Git code always worked OK for me.