Whoa, these do look like strange attractors! Especially the one at 2:37, the spirals there almost remind me of ones you see in Mandelbrot sets. Also... Debussy's First Arabesque is one of the few pieces I can still play on the piano, so i recognized it right away heehee

@tygermarez2556

5 жыл бұрын

of course id see you here lol.

@CodeParade

5 жыл бұрын

Debussy is my favorite classical composer, I also learned to play First Arabesque and Clair De Lune.

@Magnogen

5 жыл бұрын

Hey Cary! Fancy seeing you here! Lel

@SonicPman

5 жыл бұрын

What is this, a crossover episode?

@julespoon2884

5 жыл бұрын

They are indeed related to Mandelbrot sets. Ok, closer to Julia sets actually. Parametrically, the Julia set describes all points c=(x,y) such that the set generated by the recursion x’=x^2-y^2+a, y’=2xy+b and c is closed, where a and b are reals. That said, a special case of the video described by x’=x^2-y^2+f(t), y’=2xy+g(t) would generate subsets of the Julia set at point f+g*i. Doing a transformation of this equation would give a ‘warped’, somewhat empty, Julia like object. Which is why a lot of the video’s equations here have those spirals, which btw are misiurewicz points of the recurrence. Now, the reason why it looks like the Mandelbrot set as well is because the Mandelbrot set behaves like a Julia fractal locally, which can easily be seen from the eqns that generate them.

"CODE: HELPME" I think the math is holding him hostage

@portal6347

4 жыл бұрын

FIND X OR YOUR FAMILY GETS IT

@DTorto

3 жыл бұрын

try lackno

The colors, the shapes, the music, these are legit just functions, but theyre giving me serious goosebumps

Things like these is why I decided to study math again from the start on my own, but this time, I have no tests to worry about, and I'm actually gonna put that knowledge to use now that I'm learning to code.

@kennygaming208

2 жыл бұрын

It seems like math in school was purposefully boring, I'm an F average but Im obsessed these videos and documentaries, it would be a slap in the face for me to start doing math after failing it every year of my life,

@THExRISER

2 жыл бұрын

​@@kennygaming208 My grades were awful as well, but there's something so rewarding about learning and applying math in a project, no matter how simple the concept is, don't let the education system make you hate something you're passionate about.

Quality content has been officially computer generated.

@f.jideament

5 жыл бұрын

Quality content has been logically computer generated.

@quakducc2274

5 жыл бұрын

@@f.jideament I don't see the _logic_ behind that statement *ba dum diiiiing*

@drvanon

5 жыл бұрын

This is the basis for a fun philosophical debate: obviously there is nothing wrong with your statement that this is computer generated. But whom would be the author of the art work? Do we say that the coder is the one who was the architect of the code and thus the author of it, or do we recognize the people that have worked towards building the machines that made it possible to do this. And what about the pure maths. Does that receive any praise?

@dudejoe8705

5 жыл бұрын

@@drvanon I would say that the author of the code is the author of the work, if a painter creates a work of art, the credit goes to the painter, not the person who made the paintbrush or paint itself.

@vbgvbg1133

4 жыл бұрын

drvanon I can do one better, *if the machine is somewhat intelligent, is it the author?*

3:00 Are you okay, CodeParade?

@CodeParade

5 жыл бұрын

Hehe, I was trying some funny codes as a joke, but I liked how it looked so much, I had to keep it.

@oscill8ocelot

5 жыл бұрын

@@CodeParade That's just what someone in distress would say to throw off the scent! =P

@Woetson

5 жыл бұрын

@@TheBigLou13 Wooooosh

@Woetson

5 жыл бұрын

@@sussybaka3603you're*

@isabelle5547

5 жыл бұрын

PixelTheif "Haha, you're correcting me in a youtube comment section. Fucking Loser." "Oh... I'm also going to correct you." how desperate for attention do you have to be lol

This is quiet beautiful and dramatic. PRQSTS OGIUOC OHSHIT

@taxxon_

4 жыл бұрын

OH SHIT

@DanaTheLateBloomingFruitLoop

4 жыл бұрын

The first one is giving me interdimensional-dickbutt-vibes. I know the meme is long dead but I can't help it.

@alexanderliang2437

4 жыл бұрын

@@taxxon_ XD

@danny.belanger

4 жыл бұрын

You just break my brain

@lachainedudeveloppeur2556

2 жыл бұрын

MAXIME is also beautiful

Teacher: today we are going to start with algebra My brain: chaos equations

@swine13

4 жыл бұрын

Would you like to upsize for $1? *chaos equations*

@Open6a-fx4qf

4 жыл бұрын

My brain : a black hole?

@joda7697

4 жыл бұрын

Algebra? That is a calculus thing. Those are literally differential equations.

Cool! My profile picture came from doing the same with a function called an LSTM in machine learning, just recursively applying it to a point cloud. It’s surprising how complex these patterns in your video can be coming from such simple equations! Thanks for sharing, love your work.

@CodeParade

5 жыл бұрын

That's really neat, I never though to do it with neural networks.

@giantneuralnetwork

5 жыл бұрын

CodeParade Yeah! Thought it’d reveal something about their inner structure or modeling power but in the end I just got some pretty pictures :-) I think the patterns did change a bit with different activation functions or bigger nets, will have to revisit it sometime.

@WildAnimalChannel

5 жыл бұрын

Interesting. Well the input would be a vector V=(x,y,x^2,y^2,t,1). And then you'd apply M^n V where M is a matrix of weights. But in a neural net you'd also apply like a sigmoid function. Yes, I can see the connection. So it's like these are patterns represent the complex things an recurrent neural network can replicate. Maybe even be Turing complete with very precise input values. Fascinating. Maybe you'd have to allow quadratic neural networks instead of just linear ones even though. hmm...

@mauroacosta5115

4 жыл бұрын

@@giantneuralnetwork hey! I Have a question where did you applied the functions (sofwares)? Do you if it can be done on proccesing?

@giantneuralnetwork

4 жыл бұрын

@@mauroacosta5115 I did it in python in a jupyter notebook! I used opencv to plot the points in an image after. You could do it in processing but you'd have to implement your neural net there.. while many neural net libraries exist for python.

Next project; 4d game engine

@CodeParade

5 жыл бұрын

I'm legit thinking about it. It's been 10 years, and Miegakure still isn't out!

@ShroomLab

5 жыл бұрын

@@CodeParade I once made a 4d ray tracer, you can have the code

@henryseg

5 жыл бұрын

CodeParade There’s more than one way to do a 4D engine!

@codynelson424

5 жыл бұрын

@@CodeParade I made a 4d minecraft clone

@aldobernaltvbernal8745

5 жыл бұрын

@@ShroomLab can you please share the github link? I would love to experiment with it!

for me, this is one of the best definitions of beauty

This is one of the most beautiful things I’ve seen on the internet in a long time. I’m amazed by how simple it is and am so glad I was able to see it. Great choice of music too!

This channel is such a hidden gem! Awesome stuff.

@fitradical

5 жыл бұрын

Yeah

That is not 'Simple Mathematical Art', it is awesomeeeee

@CodeParade

5 жыл бұрын

Simple in the sense that it is simple to make, like the Mandelbrot set.

What’s really cool is that you could see these as cross-sections of 3D fractals.

it was beautiful to watch, the music fits well, good job dude, thank you for making this

Thanks for uploading this. I'm doing research for my own amusement but also for the purpose of putting together a video for a scholarship contest, so I can go to school to study physics. I'm thinking of making my topic Chaos theory, and so a search brought up your video. It's so lovely. The way some of them got increasingly clomplex and then seemed to dissolve or evaporate, leaving a shell behind which gradually became a simpler and simpler outline until they seemed to spiral down a drain and poof from existence is just breathtaking when paired with the music. I know others have said it, so I'll just confirm; the music was a great choice.

Magnificent. I do love your creative activity.

chaos equation's: *chaotic yet beautiful*

Amazing to see your code and eqations visualized. Great work!

This is so beautiful O:

@tgfjrfjfgjgfj

5 жыл бұрын

If you try the code : CHAOS_ you got a perfect circle at t=0. What a coincidence

@dudeawsomeness1

5 жыл бұрын

I thought you were wilburgur

@ivarangquist9184

5 жыл бұрын

Hey, I recognize you from GM48. The internet suddenly feels smaller.

@WangleLine

5 жыл бұрын

@@ivarangquist9184 Oh, that's sweet, nice to see other fellow gm48 people over here! :D

This reminds me of Chaoscope, some program I used to toy with attractors years ago. Really fun to play with

Why is this channel still slept on? Keep it up man and you will be rewarded 100%

Just beautiful stuff as always. I love your videos!

As someone studying MIS with no idea what I want to do in life, I'm really drawn to these videos and wish I would have taken a path like this for life.

The universe is just a complex chaos equation and i love it

Awesome music choice :) and a very cool video to boot!

I could cry, it's so beautiful... The forms, they just make sense

Studying this for 3rd year engineering at university, we call them "Nonlinear Dynamical Systems", with attractors being a subset of that categorization I believe

What I find amazing is how many cosmic things look like many of the demos. I saw spiral galaxies and solar flares a lot in this

Good choice of music! Man, didn't knew Debussy's Arabesque 1 would really fit the theme of mathematical art. Just so damn amazing

This is amazing! Thank you for sharing the code/program

Amazing. I used to try to make these back in 1989. My computer was just too weak and slow to get this kind of look. These are amazing.

I could be totally wrong here, but the use of "t" as a third, outside variable kind reminded me of parametric equations. Maybe this is a just a really cool way to visualize them. There might be something more to it, though, judging by how you use those same equations to generate the particles (like nested functions).

@josecontreras3396

7 ай бұрын

A parametric equation is where you define the x and y with a third parameter so they kind of are parametric equations

this was one of the most beautiful videos I have ever seen

I'm so glad your channel is finally getting the recognition it deserves xD been a Sub since 6k which wasn't that long go

When math is better at art than you

@f.jideament

5 жыл бұрын

What do we call it as? Mathist?

@votemefordictator4910

5 жыл бұрын

@@f.jideament Martist.... Artician... Arthimatician?

@TernaryM01

5 жыл бұрын

@@f.jideament Generative artist en.wikipedia.org/wiki/Generative_art

@DiamondSane

5 жыл бұрын

math is not, it's not artist, but a tool

@nivlescollection3509

5 жыл бұрын

Artmathist

The music makes it even better.

I really love this channel, keep it up man

Beautiful! I love the music. It's a different perspective for me. Thank you for sharing.

Some of the ones I have found I like recently are: ABSURD, HIGHER, and BOTTLE

It's beautiful...

Beautiful animations! And excellent choice of music :)

This makes the universe make sence

Some of these look like the lifespan of some sort of deep sea creature made of bioluminescent nerves, very weird how even random equations can form these beautiful organic patterns ! Thanks for the upload this was very well displayed👌🎥

I don’t know what it is but something about this makes me feel incredibly touched

@Kycilak

5 жыл бұрын

Probably the music

I don't usually post comments, but I just wanted to mention I love your work and you're an amazing and talented person! It's a lot of fun listening to your explanations and looking at your creations. Keep up the amazing work! =D

breathtaking. thank you for sharing!

In the future, entertainment will be randomly generated

@igorchistyakov8876

4 жыл бұрын

WEED EATER

@jinjunliu2401

3 жыл бұрын

I love how this is suddenly everywhere while it's from 2001 or so

@Hello-qg4yk

3 жыл бұрын

Yeah

Just learned about these 2 hours ago, (well i heard of them). And now you have a video out.

Beautiful - from Galoise to Lorenz to Feigenbaum.... it never gets old.... thank you....

My dude, you are an inspiration for so many of us viewers.

I guess the technical term for these equations in nonlinear dynamics would be "a family of discrete chaotic maps". If you want to treat them as a dynamical system your t is not really time. Instead the time is characterized by the number of iterations n of the equations. You start with a point (x_0, y_0) = (t,t) (initial condition) and each iteration of the equations (the map) gives you the next point on the trajectory. In other words you have (x_n+1, y_n+1) = f(x_n, y_n) which is a discrete map because the "time" n is not continous. If you look at the result for some fixed t you are looking at one trajectory of the dynamical system up to the time n which equals the number of points you draw. Because your map also depends on t it is actually not a single map but a family of parameterized maps. You could say if you change t you are changing the "laws of nature" by which your dynamical system operates in a controlled manner. A well-known one-dimensional example of what you are doing would be the logistic map en.wikipedia.org/wiki/Logistic_map where the control parameter r corresponds to your t. All of this also means that you are indeed looking at strange attractors in many of these images.

@topchrischang471

2 жыл бұрын

So What it's going to be called if it is a 2D version? We currently want to parallelize this algorithm using Parareal en.wikipedia.org/wiki/Parareal and wonder if it is possible to do that. It would be great help if you can answer this. Thank you!

@nictibbetts

Жыл бұрын

Cringe

Could you use "t" as a Z dimension and show those shapes as 3D entities? Because right now they look like cross sections of some interesting things :)

this is truly beautiful. Thank you.

Equation is a true magic and then solving the equation and realizing everything is related is mind blowing.

They’re like the awesome old screensavers that became the only redeeming quality of elementary school computers! (Just better!)

Music: Arabesque by Debussy

this what the people needa see. much love man 🙏🙏

This is one of the best channel ever.

Nice! Love to add a z axis and see what cool stuff happens in vr

@IsraeliXdude

5 жыл бұрын

Dont you mean 3D?

The coefficient for each term is either -1, 0 or 1, and each iterative equation would have variables x^2, y^2, t^2, xy, xt, yt, x, y and t. That gives us 3^18 permutations, and you used one letter of alphabet along with an underscore to contain 27 combinations, in order to use 6 letters to represent all possible combinations. Neat. Wild guesses below: x^2, y^2, t^2, xy, xt, yt, x, y, t coefficients for x' correlates with the first three letter, while the nine coefficients for y' is contained by the latter three. _ is (-1,-1,-1) for the three terms it corresponds, and A is (-1,-1,0), D is (-1,0,0), so it increments by balanced ternary system.

dude. this is beautiful

Lovely. Thank you for posting this.

This is very beautiful.. Btw, if you're interested, I think these are modili spaces for the orbit under a certain polynomial dynamical system.

They might not be strange attractors, but some of them are attractors nontheless. If we consider the x-y-plane as the phase space with x = x and y = d/dt x you just modelled non linear systems. This is pretty common in numerical physics.

You sir, you created something magnificant!

This is so cool and crazy to me. This is literally how I always pictured the band Orchid’s music, and their debut album was called Chaos Is Me. I think you picked a great name !

3:37 looks like the visual representation of the golden ratio as seeds in a flower that Numberphile did a while back. 🤔

@naoEOOjimo

4 жыл бұрын

It looks like a portal

@thomasbauden198

4 жыл бұрын

Or just infinite density before infinite expansion of the universe

Reminds me of lissajous patterns. Have you tried adding trigonometric functions to the mix?

@user-lt2rw5nr9s

5 жыл бұрын

Maybe someone will add them to the source code

@jackbrand4507

5 жыл бұрын

God I want to see that so badly

@charleslambert3368

4 жыл бұрын

You don't need trig for lissajous. Just some extra hidden variables behind the scenes. y'=y+dy x'=x+dx dy'=(1-C)dy-Ay dx'=(1-D)dx-By A and B are close to a whole number ratio (e.g. 3 and 2.01). C and D are small or zero. Or get some broomsticks and weights and build a harmonograph.

@ineednochannelyoutube5384

4 жыл бұрын

Trygonometry all just boils down to the cosine and Pythagoras laws. They can be expressed algebraically.

@benedictus5657

2 жыл бұрын

im writing my own version of this in julia right now, if you're still interested i can show you the results with trig functions :)

criminally underrated channel

The most beautiful thing I've ever seen 🔥🔥🔥

Would be great if you make a full tutorial on one of these!

Was that Desmos in there? At around 1:10

@CodeParade

5 жыл бұрын

Haha, yes it is! I was too lazy to animate it myself :)

@kangar1797

5 жыл бұрын

Desmos will conquer the world mouahshaha !!!!

@telecorpse1957

5 жыл бұрын

@@kangar1797 It's funny how I have just added Desmos to my bookmarks for helping me check whether or not I solve equations/inequalities correctly.

@ittotaq

5 жыл бұрын

@@telecorpse1957 There's an app too.

@user-ro1cc8tz6d

5 жыл бұрын

You can do the same with geogebra but i should check desmos too

Phenomenal my guy, well done. Thanks for sharing.

This look amazing on an OLED display

These are awesome, they look like fractals but they also look like a sliced pieces of a 3d structure as the time progresses , im pretty sure that if you put time in a vertical axis it will be a structure! Trust me i'm a sculptor :P

@Mlksgf

4 жыл бұрын

@meme I didnt know what these functions where until you said it. Thanks for the info! Parametric area is beautiful!

I was thinking, would it be possible to do the same, but it uses music to create the patterns? The first equation would be random, but the second one used to determine the next position could have variables that come from the music, like the pitch, tempo, volume or something

The closing of JJPVDN (2:46) was so satisfying--it game me legitimate chills.

These are beautiful, easy album art too.

DMY_GD is one of my favorites. The reason I say "one of my favorites" is because there are still like thousands of more to see! New favorite, ------ LIIOLX ------ 0 trail persistance, 2 speed, and point size 1!

@akramaka1111

3 жыл бұрын

omg it's fricking awesome

@Exaspatial

Жыл бұрын

@@akramaka1111 haha thanks! Just revisiting some old liked videos and I'm glad to see you enjoyed it 👍

1:57 (paused) cardioid's back at it again :0!

Somewhere inside all of this is a complete understanding of the entire universe.

The foundation of beauty is knowledge.

Cool! I used to make parametric equations on my Apple ][e. Good times! Lately, I've been experimenting with primordial particle systems. I'll post more video soon!

you need to live stream this looping

Hey, thanks for sharing this! Super cool and super simple! I've got a lot of ideas for how to use it already :D

man you have an amazing channel

I'd like to recommend making a program that automatically creates scrollwork within a drawn shape. Scrollwork is all based on formula and mathematics, but takes talent to actually draw it out. I feel it could be done via computer if someone decided to make it software for it. That'd be amazing!

so the characters can be devided in 2 groups group a and group b group a controlls x and group b controlls y setting one group to MMM will result in 0 for that axis when group a and group b is identical a 45deg line will be drawn

The music makes this amazing to watch!!

Differential Equations. Beautiful.

Very nice work! I read a book in 1993 "Strange Attractors: Creating Patterns in Chaos" by Julien Sprott that created 2D works based on higher dimensional projections that looked a lot like these, and they also had been given letter codes to generate with the software that came on diskette with 3D-Glasses! Check it out!

it would be nice if you could pan around some 3d versions of this

@CodeParade

5 жыл бұрын

Yeah, the algorithm generalizes very naturally to 3D. Maybe I'll explore this in the future.

@SpektralJo

5 жыл бұрын

@@CodeParade couldnt you create the actual Lorenz atractor then?

@xenontesla122

5 жыл бұрын

SpektralJo (Edit: You could do it because the Lorenz attractor is 1st order.) That’s based on differential equations, so a point in space won’t always go to the same next point (depending on speed). But here it always goes the same point.

@zoltankurti

5 жыл бұрын

@@xenontesla122 you are wrong. In case of the lorentz attractor, it only depends on the point since it's a first order equation. You are talking about second order differential equations, those need position AND speed as initial conditions. Not first order ones.

@zoltankurti

5 жыл бұрын

@@xenontesla122 and this also is based on differential equations...

I have no idea how surprising a simple equation can be! I always work with them and they always surprises me! I love math!!!

Breathtaking.

Hi! I have a question about the points. When you create a new point, does it always start at the coordinates x = t & y = t ? That is, since t, time, is always changing a bit more, the new points always appear in slightly different parts, right?

3:00 "Code: HELPME" Also these would make really cool loading/menu screens for a game

Terrence McKenna lectures brought me here lol... It's funny how I never liked math, but watching stuff like this makes me want to understand it more... Really wish mathematics wasn't taught so boringly in school.