Awesome Math Animations

Fantastic animated visualizations of mathematical mischief and tomfoolery.
♪ Endlessly gazing in nocturnal prime,
She spoke of her vices and broke the rhyme.
But baffled herself with the final line,
My promise is made but my heart i-is thine.. ♪
This video is a part of the series.
Playlist: • 🖋️ Maths
Graphing calculator - desmos.com/cal...
GRAPES (software) - www.criced.tsu...
enderman.ch

[@xloppyschannel4881]

Can you upload a 3d version?

[@gallium-gonzollium]

@@Andrewman Geogebra?-

[@50Steaks68]

@@Andrewman wolfram mathematica feels like its own separate programming language. That's why I am not a fan

[@prestonwhite6423]

Geogebra is the best free 3d graphing calculator out there

[@potato686]

@@raulsilva3730 i dont think blender fit for this, if he wanna do this in blender it would have to be geometry node or python and eitheir what he choose would take lots of time

[@katagiharaimotouge]

6:09 まさかだけど主日本人？w

[@gallium-gonzollium]

The nostalgia of making random graphs until you find something cool.

[@Zedryx69]

True.

[@hunteractually3637]

How can you make those graphs? You mean like on a piece of paper or some program?

[@markusalonso3163]

Yup I had a sheet in Desmos where I made as many different thing as I could and then tried to get them all in all 4 quadrants and in both directions

[@supersonictumbleweed]

Ken Silverman's 3d calc

[@put544]

@@Zedryx69 FALSE CUZ STALIN IS NOT HAPPY NOW

[@tristanmiller6598]

I love that I'm not the only one with the overlap in interests of death metal and math

[@妛槞]

I never really considered Opeth death metal. I guess Orchid was close to death metal

[@DaButter2.0]

@@妛槞 That's because they are prog, not death

[@nbd9321]

@@DaButter2.0 although it's not pure death metal they still use a lot of death metal elements in their early stuff, they're both.

[@dasapples]

Michael also did bloodbath, so at least we know they like it

[@RandomEG1234]

Well death metal, uhhhhhhhhh, but i do love math

[@sawyerjacobson1]

I think it’ll be interesting when graphing calculators get better to see how these graphs compare. Maybe they look completely different,

[@draido-dev]

Interestingly, the project we are working on is this, making a graphic calculator that is able to do graph animation of graphs, be using some powerfull arm cpus, i just found it weird that someone wanted that to happen, we are thinking to put things in kickstarter but, we always think no one intrested, and the fact that people stop using TI-84 and instead using desmos etc

[@macicoinc9363]

@@draido-dev yeah, why specifically arm cpus? Just make a C++ version of Desmons so it doesn’t run horribly and devour your ram and then make it so you can partition the graph for computing and save them. You could get so much detail from them it’s insane. You could also upload the files so people mess around with them. Would be pretty easy to make 3D as well.

[@Evan-hm7tz]

I believe that you could just have a simple software and render it like people do with fractals, and just have it plug in super super small values and forces the pc to keep the floating point, and then save what the equation spits out, then just graph it with something that uses the entire floating point.

[@puppergump4117]

@@Andrewman For most graphing calculator uses, you don't need the precision of a 64 bit floating point number. The only advantage x64 provides is more RAM that can be used. With x86, the cpu can use 2 addresses in a single 64 bit register. I think there's also loads of other optimizations. The biggest advantage with ARM specifically is the multithreading capabilities, but I have no clue how you'd divide the calculation of a single function. Maybe one thread per graph rendered in a moving thing like this. Anyways, those little optimizations are probably for extreme use-cases. But what I do know is that x86 won't go away. It's used in too many little things.

[@myrjavi]

@@draido-devis there progress on it?

[@musclechicken9036]

0:52 fun fact: every single function output for each arguments a and b on this function can be described as a plane cross section of two cones shaped like an hourglass. This is basically what conics is.

[@acelix3087]

huh? what axis? it can't be vertical axis cause the circle part can't be on a plane section, can't be horizontal either cause horizontal is just circles, i don't get your point

[@meepoffaith6153]

@@acelix3087 We have 2 cones pointing to each other each other tip-to-tip slice it at some angle to get different cross sections if the plane is flat, it passes through one cone and yields a circle if the plane is at a slight angle, it still only passes through one cone but now yields an ellipse if the plane is at a steep angle, it passes through both cones and yields a hyperbola

[@macicoinc9363]

@@Andrewman all you have to do is go into geobra, graph z=x^2 + y^2 and then make a plane based on a and b.

[@Neo-vz8nh]

The solution of celestial mechanics, the two body problem.

[@aleph1192]

@@acelix3087 The animation is similar to that of the cross-section between the hourglass and a plane rotating on a non-vertical axis.

[@nathanhelmburger]

I like that the "hearts" graph has a squiggle in the moddle which kinda looks like the ekg trace of a heartbeat

[@bertberw8653]

Wasn't expecting to hear Opeth in a math video, it just made everything 1000x better.

[@silverphoenix_1756]

Same dude, it felt like hallucinating

[@camerongearhart8156]

Bro i made basiclly the same comment then scrolled down and saw yours. 😂. Seriously though opeth is great

[@diegodecanini9248]

i also check if i put it random on my cellphone or something , wasnt expecting opeth neither.

[@Shane-5229]

​​@@diegodecanini9248Could you tell me what song it is please?

[@diegodecanini9248]

Face of Melinda - Opeth - Album: Still Life.@@Shane-5229

[@EmmaHopman]

For me I noticed that with an extremely strong PC CPU it shows much better, also zooming in on rough lines will make them smooth some.

[@Cairillic]

Every time you return to the same topic, and every time you have something to surprise.

[@zirc0n]

this math gameplay is insane 🔥🔥🔥🔥

[@kyyay-yt]

seems like the "circle filled with sine wave" at 2:12 is actually filled with more circles

[@xelalexa3262]

those inner circles arent so circular but yea

[@omerd602]

@@Andrewman They don't seem to be ellipses either, they're just some shape that doesn't have a name

[@omerd602]

@@Andrewman The general conic (including ellipses) is a degree-2 algebraic curve, so essentially just ax²+bxy+cy²+dx+fy+g = 0. Both x² and y² can be represented with this, but there is no way to write bsin(ax) as a polynomial, so they cannot be ellipses. (Also, if you pause at the right times, sometimes you'll be able to see slight horizontal asymmetries in the shapes, which can't happen with ellipses) EDIT: The reason they are so similar probably has to do with how the positive part of a sine wave looks like a parabola, which is a degree-2 algebraic curve. If they were actually parabolas I think you would be getting true ellipses

[@ChraO_o]

@@omerd602 ellipses are ellipses, it's just that it's connected via wave but tbh I don't think it's ellipses despite the fact it also looks like it is💀

[@BurrritoYT]

no way its celua developr!1!1!1!

[@C_Corpze]

Love how it at some point becomes straight up fractals.

[@Sebalou622]

2:20 that is one of the coolest graphs ive ever seen wow. Great work, and great video :)

[@SylvainBerube]

Always interesting to see your creation, thanks! I teach calculus and I show your video to the students when we start to work with implicit function.

[@tedsheridan8725]

Hi Sylvain, I just created a calculus video I'm planning on uploading not YT, but am hoping to get some feedback from calc teachers (esp calc 1). Would you be willing to watch it and share any thoughts? Thanks!

[@pascallaue16]

Pov: You rubbed your eyes too Hard 3:53

[@MrBratello07]

Man, this soundtrack is SHREDDING!

[@omerd602]

Pretty sure your stuttering curve is only stuttering because you gave the variable A a step-size of 1, so it's not moving continuously

[@StuffandThings_]

Is it just me or would 6:11 be *fantastic* for video game random generation of structures? Like, you get randomized points with what seems to be a pretty random scattering too (other than right by the x axis), except they're not just points but have actual dimensions which could be used to map out the size of the structure as well.

[@CaseyShontz]

The clustering around the x-axis could be useful too, for putting more things around a major road or pathway

[@hotpotato5587]

The only problem I’d see with this is since it’s based on trigonometric functions, so wouldn’t it repeat rather quickly?

[@waldolemmer]

🐌🐢

[@StuffandThings_]

@@hotpotato5587 That could probably be dealt with by simply choosing a random portion of the scatter, like how seeds are used for typical generation based off of equations. It would also allow for some amount of predictability or repeatability if desired.

[@prestongarvey2599]

@@StuffandThings_ so basically its a non-true random generator picking numbers from yet another non-true random number generator to present itself as random generation?

[@clinn]

this is hypnotizing and scaring at the same time

[@abowlofnoodles946]

I can feel the pain desmos and grapes go through to just display these

[@jaydencrimsoneverett6731]

0:25 Better Call Saul moment

[@_TheGreenCode_]

This is why I get confused when someone says they hate math, there is always something mesmerizing…

[@radkiel]

Was not expecting Face of Melinda but I’m pleasantly surprised

[@WaluigiisthekingASmith]

The circle filled with circles reminds me of a common representation of a wave function in quantum mechanics

[@lucienzothesmallerone]

As a person who loves music, I legitimately said "Wake up babe, new Arctic Monkeys album dropped" in my head as I saw the graph

[@dragon_draws]

i really feel like some people just type things into caculators and waits to see what happens

[@mikecharecky2818]

This was wonderful, gorgeous function plots and face of Melinda to top it off :) I was absolutely hooked

[@BryndanMeyerholtTheRealDeal]

3'00 It won't stutter if the a parameter isn't fixed to integers

[@Its_Zer0here]

3:28 this can be a good loading screen

[@rosethornfox801]

I love how humanity has managed to make graphs so complex that fucking graphing sites and a hard time/ cant even process them

[@cretaceouscrabrevolution5644]

Came here for maths, stayed for music. Absolutely amazing music choice!!

[@sawyerjacobson1]

Geometry dash, math, and a Fate profile picture… this channel was meant for me

[@CombustibleL3mon]

I love the well-timed drop in the music 🎶 when level 3 starts!

[@cinnamoncat8950]

the drop jumpscared me

[@olegmoki]

@@cinnamoncat8950 math jumpscare

[@mr.shroom4280]

This is the most interesting math videos I've seen, please post more

[@pierrefrebet5630]

Came for the math, stayed for the music

[@DiamondSane]

i just thought it's something familiar, and then i realized it's opeth. nice meet

[@katharinahasenbalg8011]

name of the song? pls

[@DrDrake-lq8nh]

@@katharinahasenbalg8011 Face Of Melinda - Opeth

[@redisanuber]

Came for math left because the music

[@katharinahasenbalg8011]

@@DrDrake-lq8nh thanks!

[@Reycko]

really love this series

[@Guys-s5v]

I am a desmos user and a not so popular youtube chanel (at 2023, if you're looking at this 20 years from now and wonder why it's different) - i bet these can grab people's attention! Thanks! I subscribed!

[@Sedi3D]

Try this one: a\left(x ight)=\frac{\frac{\tan\left(1 ight)}{10x}g\sin^{-1}\left(\cos\left(x^{\left(xg ight)} ight) ight)}{2} Set the g variable slider to the lowest value of -30 and the highest value of 20. It'll create a wave-like pattern and then create a small wave pattern.

[@J.K-j2g]

I really didn't like the math classes. But to see dynamic graphss like these, I finally do realize what they meant... Thanks for the good works!

[@allankaige7364]

Wow thats amazing. There are so many beautiful graphs!

[@DustinGunnells]

The music is exceptional!

[@silentsuz]

i believe that a function is very silly if desmos cant run it and grapes straight up crashes

[@Dubile]

4 months ago, this video introduced me to my favorite song. Absolutely blew me away the first time I heard it.

[@macicoinc9363]

I like the music and slideshow nature of this, reminds me of old KZbin.

[@porcelainstorm5397]

awesome video! i'm so curious at 6:17 if there is any relationship between the generating of the circles and the logistic map, since it seems like chaotic behavior. also really interested by the roughness of some of the lines, would love to zoom in and see if it's rough all the way down (fractal) or smooths out with zooming in. great video and i love the music too

[@livek1238]

When world most needed him, he returned

[@pps7642]

Perfect choice of music. Love that band. Edit after watching: I liked 4:30, The dance of Tangent Curves.

[@harelsagy2992]

Wonderful video, love the Opeth background. Now think find the most brutal and sadistically complicated graphs to display on a Cannibal Corpse song 😂

[@brodie3029]

WHOAH THATS SO AWSOME I CANT BELIEVE I JUST SAW THE MATH ANIMATIONS :3

[@Cole-li7hq]

Face of Melinda and cool graphs, boss ass video

[@happiness4919]

00:25 Logarithm of a variable line 00:39 A springy function 00:51 A variable pythagorean function 01:14 An elliptic curve. Often used in cryptography. 01:33 A hyperelliptic curve. The general case of an elliptic curve. Level 2 The parameter change yields sophisticated or hardly predictable movement 02:07 A circle with a variable radius filled with a sine wave of a variable density 02:31 Infinite field of hearts. by XLTheCoolGuy 02:47 Actual audio spectrum! by SakaroZ 02:59 The stuttering curve. Looks like a Desmos-only quirk 03:24 Looks like an optical illusion 03:45 An affine plane consisting of different curves. Mesmerizing! Desmos fails to display this one. I'll use GRAPES. Level 3 Unpredictable graphs that even Desmos is struggling to show. (or, even fails completely 04:33 The dance of tangent curves. by Hory 04:59 Symmetric curve tunnels. by Anticiobster831 05:25 From this point on, I'll just stick to GRAPES, as Desmos doesn't seem to do the job at all 05:45 Stalagmites. The inequation crashes GRAPES. by Y!KES (was-not-found 06:12 The random point generator. 06:38 The parametric tangent spiral. 07:04 Ancient alphabet. a = 2; b = 2

[@legate7158]

r = Sin (a/e * theta) a = e 2e an everchanging circle. You can replace the sin with other functions like csc and floor that equasion to get stunning circles

[@Ryguzapi]

As a guy who's not really into metal, Opeth is a great band

[@maximus0wls6415]

I got recommended this video at the perfect time cuz we r learning about cardioids limacons roses and lemniscates in honors precalculus and i really enjoy them so this video made me happy

[@BalthazarMaignan]

That's what I ask for when I open KZbin

[@akuma_tenshi6176]

Late night just scrolling through youtube and found this, really neat and i love the music, i pairs so well! Have a day, i can force you to make it good, just have one.

[@thejaeger02]

I have to say the song playing in the background was amazing

[@nethe1096]

This music goes *absolutly perfect* with this video

[@towel2043]

I did not expect to hear Opeth when clicking on this video, but I must say I am not disappointed

[@wyboo2019]

i know there must be some hidden mathematical gens somewhere in these weird graphs; the graphs might have absolutely not applications but im sure answering questions about solving one of the equations, finding integer solutions, series representation, and etc. must yield something interesting

[@boochin]

You forgot the topologist's tan curve! f(x)=tan(1/x)

[@johnnyswatts]

Beautiful stuff! Just a quibble on nomenclature: a usecase is not a use. Usecase has a specific meaning in computer science that is not synonymous with use or useage.

[@Lax512]

Bro this just scares and frustrates me because I cannot understand how any of this works at all.

[@wiez543]

Awesome how beautiful math can be :)

[@Dynamite___Harry]

Excellent choice of music :D

[@GalaxyStar-z2c]

Very cool. Was planning to learn math when I havve the time. And do these when I have enough knowledge

[@gigajet3390]

Bro this is what you see when you fall asleep for 1 minute in a maths class

[@JayPon629]

here is a cool but random equation to use: y=\frac{\left(\tan\left(x ight)+\sin\left(x ight)+\cos\left(x ight) ight)}{\csc\left(x ight)+\sec\left(y ight)+\cot\left(x ight)} just copy this and put it in desmos

[@5ilver42]

Thank you for introducing me to this band

[@voidentityUTX]

PLEASE GOD UPLOAD A VIDEO ON HOW TO GRAPH A CIRCLE AROUND A POINT TO MAKE IT MOVABLE I BEG OF YOUUUUUUUUUU

[@the_m_original]

@@voidentityUTX (x+a)^2+(y+b)^2=r i think a,b - point coordinates r - circle radius

[@durtt]

I just stumbled into the maths side of youtube. Trying to read any of the comments in this video makes my brain ooze

[@v_lad8559]

I half expected a live cam of grapes in a stop-motion thing lol

[@bartodziej5763]

Oh my goodness, didn't expect Opeth here

[@CombustibleL3mon]

Would be cool to see some differential equation solutions graphed with varying initial values

[@deleetiusproductions3497]

2:59 It seems one of the values is only changing in increments of one.

[@meks039]

level 3 looking metal as fuck. The most metal maths will ever get

[@patchbyte6856]

Actually thank you, this is so f-ing nice

[@Blueoceandog]

With the music playing in the background, this is giving old-school Windows Media Player vibes.

[@cougher9000]

cos(ac) ------------- gets bigger the less A there is (i think this is because if something is divided by 0, it goes to Infinity) try it (also use the default variable for c) or just use X or whatever to replace the c a

[@limenlemon3116]

I love how the graphs x+y+1=1 and x=-y are the same

[@vovancho]

It's because: x + y + 1 = 1 x + y = 1 - 1 x + y = 0 x = -y

[@rushasley7409]

Me too i like The stuttering curve. Looks like Desmos-only quirk

[@thefounder681]

I've seen a lot of mathematics over Tool... but Opeth is a new level

[@후크남친]

2:34 i love it❤❤

[@댓글용계정-k9j]

호야가 귀엽긴 해요

[@thenarwhalmage]

6:12, this one actully kind of works better on desmos if you zoom in a bit. you can see it makes a bunch of concentric circle-like things around the origin

[@yu_a_vi4427]

thanks this is quit helpful when playing with functions using shaders

[@thescooshinator]

A bit late, but (0t,0) is interesting. It only takes up one point at (0,0), but you can actually see the point unlike most other equations like it.

[@adreq3.05]

Ideal modulation for secret messages.

[@k4x1rda41]

this man deadass making an extremely useful video with opeth in the background what a fucking gigachad

[@ChongCMfan]

The only thing I could think of using my 2 brainchild is that how this man's PC survive all of this

[@airy9461]

Bro I did not expect to click on a random math video and then be met with Face of Melinda in the intro, I thought I accidentally clicked on one of my music tabs!

[@rubensf7780]

Nice choice of music

[@joannawesseling5261]

just so you know on desmos you can remove y= and it will be the same unless theres y on the other side

[@cameroon5404]

who would be so bored as to experiment enough with this stuff

[@mantacid1221]

Mathematicians.

[@basstringer5586]

Came for the math. Stayed for the Opeth.

[@Khanh1200]

The Dot Generator looks like I'm flying in the MK galaxy.

[@Chromed111]

I used to make this stuff in math during high school

[@shiftsky7130]

funny that you turned to your inspiror (hi shibachi) who used GRAPES when desmos failed

[@nuts5388]

Desmos shows a lot of these just fine for me and grapes seems to be only on windows vista and older

[@FoxDog1080]

5:32 this works fine in Desmos

[@zayefislam1338]

5:26 For some reason, when i tried to render this graph expression inside Desmos, it actually managed to render it on first attempt.

[@mustafapehlivan5856]

try this equation i found: x^{31}\cdot\left(y-x ight)+\left(x+1 ight)^{32}=z it's EXTREMELY ULTRA long so change the range of "z" from 1 to 10^15 or even higher than that you can change the exponent of "z" if you want and this equation (it's awesome): \frac{x^{3}-x}{x-1}y=z you can change the exponent of "x" if you want