Amazing graphs dictated by mathematical rules, now in the animated format. This video is a part of the series. Playlist: • 🖋️ Maths Graphing calculator - desmos.com/cal... enderman.ch
0:18 Laser/Scanner 0:24 Rocking Chair 0:30 Flickering Light 0:45 Neutron Star 0:57 Anti-Expanding Radio Wave 1:15 Ocean Waves 1:26 Bubble Sheet 1:44 Unstable Water Ball 2:05 Corrupted Noise 2:20 Ơ̶̮͔͓̙̫̦͕̱̔̏͘͜͜P̶̱̰͝E̴͍͍̦̬̲̫͉͇͙̮͑͗̄̔̓͆̄͠Ŗ̷͖̫̱̹̱̬̤̫̫̀̐̕͠Ą̴̖̝̩̜̮͍̲̟͓͐͑ ̴̢̢̰̫̺̙̝̳̀͠W̴̨͔̻̮̝̱͕̦̖̝̆̂̇̑̈̚E̶̡͔͔̥̾͂̀̅̇͘͝͝B̸̩̘̞͚̻͋͋̀͘͠ ̸̢̣͙͈͙̠͓̐͂̔̏͗͠B̶̟̄R̵̹̼̳̭̜͎̻͈͆̌̌͌̏̍͗̕̚͘Ǒ̸̻W̶̢̢̠̼͝S̸͙̈́̐͐̒́̄Ȩ̶̢̤͕̫̬̮̤̃̏͑͜R̴̳̻̰̬̀͜͜ 2:28 Tadpole's Tail 2:44 Nobody: What I see Before I Fall Asleep: 2:56 Raindrops in a pond 3:07 Every Sci-Fi "In Space" Movie Ever: 3:19 The Pinwheel of Life 3:45 Petri Dishes Be Like: 3:57 Wavering Ball of Plasma
well i certainly didnt expect at the speed of light to be the song edit: cant wait for an argument to start whether the song is from bloodbath, cataclysm, bloodlust or something different lmao
One of my personal favourites is (x - a)^2 + (y - sin(x))^2 = 2. A little blob that follows an invisible sine graph. Another fun thing about this one, the larger you make the number on the right (the radius of the "circle", the more it will converge to an actual circle).
@@Stuffinround Oh, if they mean the sine graph that the blob is following, then the sine graph should just be sin(x). sqrt(2)sin(x) is slightly off at the peaks and troughs.
I was messing with the graph at 4:10, and if you remove the plus sign in the middle of the two parentheses, you get a twinkling star. If you multiply the entire equation by big numbers, you make the star smaller. However, if you multiply by small numbers (above 0), you make the star bigger. Multiplying it by a number -n, is in fact, the same as multiplying it by the positive version n.
3:15 My favorite thing about this graph is whenever _a_ is a multiple of 5, you get all these cool flower patterns. If _a_ = 5 or -5, then you get a circle.
Wow! This is actually really interesting and I never thought that this was possible in Desmos. I was messing around in the calculator and found this: (a+x)(a+y²)=tan(x). You get an interesting animation where there's some change being transferred from line to line while a's value goes up and down.
You can graph a family of curves by typing into desmos things like a = [-5 ... 5] and you can do a lot of stuff with lists utilizing tools like list comprehension.
Thank you!!!! I use parametric to model some of my 2D animation and that “windy” graph is perfect for modeling a tail, wings or a tongue! Parametrics are my favorite!!
r=sin(a/5*θ)*2 The beautiful equation, When a=-10 or 10 : clover When a=8.3 or -8.3 : A beautiful flower! When -5 or 5 : Wormhole! When a=-1.7 or 1.7 : A beautiful race line ,but. there’s no end and one line is endable(it means it will disappear when someone runs on that LINE) When a=-0.1,-0.2 and 0.1,0.2 : vortex
Here is a nice one : x = cos(2t) and y = cos(3t+b) for -pi < t < pi You can just write it as a set of points in desmos : ( cos(2t) , cos(3t+a) ) Let a vary to animate
(X + A)^2 + (Y - B)^2 = (r^2)/(x^2) makes a weirdd animation, it's like a circle that gets absorbed by a line and then it like breaks out of the line like a xenomorph and then goes back and recombines into the circle
In order to have the average r values you must do a double integral, first for theta then for a. The coolest thing is that the first one yields to a 2(sin(xπ))/x type of integral (depending on how many whole turns (N2π) you want for θ), and from here you can youse the Feynman's method to integrate (ua-cam.com/video/s1zhYD4x6mY/v-deo.html) , but with a catch, and that is that you might have to do some workaround to find the constant, because the integral of the video isn't bounded to "a", the variable you want to have as a parameter for knowing the average 1/a' * \int_0^(a'){f(a)d(a)} But that's pretty much an analytical approach, thus you'll have to change coordinates and stuff. Also the turns are very important because with them, the expression is not a function(you might have many r values for the same theta) I would like to know what's the purpose/motivation for having the average with respect to the parameter a? if you're just looking for the average for a single a value don't mind me, I'm just curious
@@egoworks5611 so i wanted to create a way to visualize a fourier transform like 3b1b did but the normal e to the i theta integral doesnt work in desmos because desmos doesnt support imaginary numbers
@@mahanp6993 but it does support lists, so actually you can implement it using lists and functions of lists. I actually have a graph of the e^(i*theta) from that 3b1b video
One of my favourites is y=(cos(x)*-(tan(x)+sin(x^2)))^2, it's very clear near (0,0) but gets muddier the more you move away from the origin and eventually forms a line of heart-shapes.
Try( tan θc)-c (the variable doesn’t matter). Also you can try different trigonometric functions with this equation and it produces some crazy cool stuff
wow, i additionally love how this goes. with basic variables or position letter x and y, its used for graphs, code, and may types of stuff too! its much more fun with the experience of advanced math and alot more :).
i hear the beginning of "at the speed of light" and the only thing in my mind is geometry dash. it has locked itself in and is refusing to let me process any other thoughts
1:15 I can see a sine wave moving through space and this would be the slope at x=0 1:30 This one is like cutting a cone with a plane at different angles and seeing what would be left in the plane Damn, those two are really beautiful to observe
I really appreciate how the transitions are timed with the music
YES! I am a massive fan of music sync! (I do cringe occasionally on your main channel when the big drop hits but nothing exciting happens)
I really don’t appreciate you furry.
comically synced
Geometry dast
As a GD I thought I was dreaming when I heard at the speed of light lol
I'm happy people enjoy this music
These graphs are Cataclysmic!
Nice geometry dash reference lol
what will the aftermath be?
@@Andrewman and everyone will have a lust for this blood, after the catabath.
these jokes are flying over my head _at the speed of light_
@@Ja_Crispy they're being blocked by 47 dim rain drops
That one at 3:18 is called a rose curve. They're pretty cool. If you want another thing like that, the Lissajous curve might be a good fit.
It exactly looks like what I draw with a spirograph!
bloodlust
@@fandroid6491 Spirograph curves are hypocycloids.
i believe they r similar to the logic behind fourier transforms
Fun fact! The exact same graph can be found in the desmos examples under Polar:rose (i dont want this to sound sassy fyi)
2:26 this actually kinda looks 3d, like running near a sine wave
Omg, it does!
It actually does lol.
Yes...true...!!
It's Opera Browser
@@notneo7898 Opera Browser is before that
0:18 Laser/Scanner
0:24 Rocking Chair
0:30 Flickering Light
0:45 Neutron Star
0:57 Anti-Expanding Radio Wave
1:15 Ocean Waves
1:26 Bubble Sheet
1:44 Unstable Water Ball
2:05 Corrupted Noise
2:20 Ơ̶̮͔͓̙̫̦͕̱̔̏͘͜͜P̶̱̰͝E̴͍͍̦̬̲̫͉͇͙̮͑͗̄̔̓͆̄͠Ŗ̷͖̫̱̹̱̬̤̫̫̀̐̕͠Ą̴̖̝̩̜̮͍̲̟͓͐͑ ̴̢̢̰̫̺̙̝̳̀͠W̴̨͔̻̮̝̱͕̦̖̝̆̂̇̑̈̚E̶̡͔͔̥̾͂̀̅̇͘͝͝B̸̩̘̞͚̻͋͋̀͘͠ ̸̢̣͙͈͙̠͓̐͂̔̏͗͠B̶̟̄R̵̹̼̳̭̜͎̻͈͆̌̌͌̏̍͗̕̚͘Ǒ̸̻W̶̢̢̠̼͝S̸͙̈́̐͐̒́̄Ȩ̶̢̤͕̫̬̮̤̃̏͑͜R̴̳̻̰̬̀͜͜
2:28 Tadpole's Tail
2:44 Nobody:
What I see Before I Fall Asleep:
2:56 Raindrops in a pond
3:07 Every Sci-Fi "In Space" Movie Ever:
3:19 The Pinwheel of Life
3:45 Petri Dishes Be Like:
3:57 Wavering Ball of Plasma
How did you put the equations sideways overlaying the text, “opera web brower?”
@@initiald975 Website
Lol, why you wrote opera like that 😂
2:20 he doesnt need a cap for that 😂
2:56: cynosural field generator
As a GD player that knows nothing about this, I can clearly relate that this is an extreme demon
Edit: was not expecting this to get 1k likes but ok
0/10 generic hell themed extreme
The 1rt btw
too bad its extended list
What are you talking…
_video starts_
Ohhhhh….
Nah medium demon at best
2:21 wait.. its you??
opera??
I was hoping someone would point this out. 🙏
o
funny enough I'm watching it on opera
opera=best browser cus adblocker
*oracle
well i certainly didnt expect at the speed of light to be the song
edit: cant wait for an argument to start whether the song is from bloodbath, cataclysm, bloodlust or something different lmao
hi
*Bloodbath intensifies*
BLOODBATH WAT
@@UN4YA hi
No WaY
Muscle memory made me hit those triple spikes at 1:50
I smashed my keyboard hard a few times when I heard the start (the 7-13 wave is hard as hell)
This is actually the coolest thing; I haven't seen a program like desmos do this before!
Desmos can get pretty nuts if you know how to use it to its fullest potential
Bit of an unfortunate choice of a song, it would normally be ok if it wasn't heavily associated with geometry dash and will now flood your comments
it's fine
One of my personal favourites is (x - a)^2 + (y - sin(x))^2 = 2.
A little blob that follows an invisible sine graph.
Another fun thing about this one, the larger you make the number on the right (the radius of the "circle", the more it will converge to an actual circle).
Adding another one makes it look like blobs chasing each other
i found the sine graph its rolling on.
its about sine(-1.41421)
@@tesseract7586 I don't quite understand what you mean. sin(-1.41421) is a value, not a graph. Could you elaborate?
@@staticchimera44 he might mean sqrt(2) times a sin function? I’ve put sqrt(2)sinx into Desmos and it’s pretty accurate.
@@Stuffinround Oh, if they mean the sine graph that the blob is following, then the sine graph should just be sin(x). sqrt(2)sin(x) is slightly off at the peaks and troughs.
The song perfectly fits with the video
At the speed of light also known in gd as bloodbath
@@Victor_StudentOfFloppa who tf asked you?
@@Victor_StudentOfFloppa I'm tryna help a person find a song the like
Ironically the aftermath part has the best ones
@@Victor_StudentOfFloppa me
I was messing with the graph at 4:10, and if you remove the plus sign in the middle of the two parentheses, you get a twinkling star. If you multiply the entire equation by big numbers, you make the star smaller. However, if you multiply by small numbers (above 0), you make the star bigger. Multiplying it by a number -n, is in fact, the same as multiplying it by the positive version n.
It actually works!
2:14 opera browser
O
*O*
3:26 at a=pi or a=-pi the mandelbrot set's big bulb shape appears. This shape appears everywhere involving pi.
@@novygaming5713 it’s a cartoid. very common with circles and pi
3:06 Galaxy ?
*the whole big bang appearing*
OMG THAT IS SOOO COOL.
it nearly destroyed my pc 8/10
“Oh, you dare challenge Desmos?”
anime lines come into view
and no I dont watch any 😅
2:44 felt like an ancient message
Ancient aliens message
So cool to see at the speed of light as the background music. First time I do and that feels great
2:19 this video was sponsored by Opera GX!
3:15 My favorite thing about this graph is whenever _a_ is a multiple of 5, you get all these cool flower patterns. If _a_ = 5 or -5, then you get a circle.
Well yeah because then that means it's just sin of (theta multiplied by some integer)
im never letting a geometry dash player access math again
3:12 the music is well named
Speed of light?
Wow! This is actually really interesting and I never thought that this was possible in Desmos. I was messing around in the calculator and found this: (a+x)(a+y²)=tan(x). You get an interesting animation where there's some change being transferred from line to line while a's value goes up and down.
You can graph a family of curves by typing into desmos things like a = [-5 ... 5] and you can do a lot of stuff with lists utilizing tools like list comprehension.
Kinda reminds me of a photon interacting with obstacles.
Thank you!!!! I use parametric to model some of my 2D animation and that “windy” graph is perfect for modeling a tail, wings or a tongue! Parametrics are my favorite!!
r=sin(a/5*θ)*2
The beautiful equation,
When a=-10 or 10 : clover
When a=8.3 or -8.3 : A beautiful flower!
When -5 or 5 : Wormhole!
When a=-1.7 or 1.7 : A beautiful race line ,but. there’s no end and one line is endable(it means it will disappear when someone runs on that LINE)
When a=-0.1,-0.2 and 0.1,0.2 : vortex
2:55 like something dropped in a puddle also
Here is a nice one :
x = cos(2t) and y = cos(3t+b) for -pi < t < pi
You can just write it as a set of points in desmos :
( cos(2t) , cos(3t+a) )
Let a vary to animate
One I like is xa+y/a=xy. Moving hyperbola which moves outwards when a is near 0.
Also, xa+y/a=y is a diagonal line which rotates and swings back.
as someone who plays a lot of geometry dash and is literally trying to beat cata, i was not expecting at the speed of light to be playing
I immediately searched the comments for a gd reference
gl on cata!!!!!
1:42
How Italian make pizzas
Tight wave spam 2:08
My favorite is x^k + y^k = 1, for k rational. It transits between astroid, circle and square shape.
Whatever Enderman's doing, we gotta let him cook...
that clearly shows how a function can behave when a parameter is changed, very cool!
2:19 Should be Opera's logo animation
1:32 was cool bc of the song
1:31 is better
drawing the "galaxy" graph is 100x harder than beating bloodlust
F(x)= x^2/3 + 0.9(5-x^2)^1/2 • sin(ax)
While a is between 0 and 100 should have definately been in that video
And is also my thought on this video
LOL nice
(X + A)^2 + (Y - B)^2 = (r^2)/(x^2)
makes a weirdd animation, it's like a circle that gets absorbed by a line and then it like breaks out of the line like a xenomorph and then goes back and recombines into the circle
These animations are so satisfying i can’t let go of them
nice gd reference
“Galaxy”
Me: Are ya sure ‘bout that?
This has to be the best thing I've seen all day.
This will be computer graphics in 1973 😱😱😱😱
Interesting graphs! Can’t wait to see more.
@kraeon5 Im glad to hear that you are interested in them! Strange to see a viewer in the wild though lol.
IM GOING TO TAKE A BATH FULL OF BLOOD AFTER THIS VIDEO.
Sometimes, it really feels like you are seeing the shadows of higher dimensional functions
it's amazing how some math functions literally resemble a well-thought-out dance represented by lines, circles, etc
2:23 and this is how Quora was formed
1:44 bro just got born to vibe
4:00 that’s awsome
Watching those animations felt like a bloody warm bath!
The song fits so well but I’m so used to hearing it in gd it’s so funny
2:20 as an opera gx user, i like this
1:18 The Worm
wiggle wiggle wiggle
Why does it look so satisfying?
1:22 start of bloodbath
3:15 ending of bloodbath
2:00 quack
🗿🗣️‼️⚠️I can feel geometry dash coming inside of my soul ⚠️‼️🗣️🗿
Try the Wierstrass Function, it wobbles and it’s really cool!
I second this, especially from n=0 to n=a since n=infinity might be problematic
2:14 how opera made its logo
Holy cow Bloodlust
Bloodbath was first
@@AkivaB cataclysm
the music is just
*BLOODBATH*
is there a way to average the x and y values of each point for the graph r=sin(a/5 theta)? if so this would help me a lot
In order to have the average r values you must do a double integral, first for theta then for a. The coolest thing is that the first one yields to a 2(sin(xπ))/x type of integral (depending on how many whole turns (N2π) you want for θ), and from here you can youse the Feynman's method to integrate (ua-cam.com/video/s1zhYD4x6mY/v-deo.html) , but with a catch, and that is that you might have to do some workaround to find the constant, because the integral of the video isn't bounded to "a", the variable you want to have as a parameter for knowing the average 1/a' * \int_0^(a'){f(a)d(a)}
But that's pretty much an analytical approach, thus you'll have to change coordinates and stuff. Also the turns are very important because with them, the expression is not a function(you might have many r values for the same theta)
I would like to know what's the purpose/motivation for having the average with respect to the parameter a? if you're just looking for the average for a single a value don't mind me, I'm just curious
@@egoworks5611 so i wanted to create a way to visualize a fourier transform like 3b1b did but the normal e to the i theta integral doesnt work in desmos because desmos doesnt support imaginary numbers
@@Andrewman r² = x² + y²
@@mahanp6993 but it does support lists, so actually you can implement it using lists and functions of lists. I actually have a graph of the e^(i*theta) from that 3b1b video
I love how Opera paid math to have their logo included in one of the functions
Pretty cool! I'm waiting for more
One of my favourites is y=(cos(x)*-(tan(x)+sin(x^2)))^2, it's very clear near (0,0) but gets muddier the more you move away from the origin and eventually forms a line of heart-shapes.
it works without the negative sign as well :)
Hmm this song sounds like geometry dash
Going into this the thing I least expected was At The Speed Of Light to start playing lmao
Try( tan θc)-c (the variable doesn’t matter). Also you can try different trigonometric functions with this equation and it produces some crazy cool stuff
you mean r=(tan θc)-c?
Good music because we all know math is as hard as bloodbath
h o l y s h i t
is that a MOTHIER
FOOKIN
GD REFERENCE?!?!
aAaAaAaAaAa
Really appreciate for Geometry Dash music (Dimrain47 - At the Speed of Light)
I’m only here for the GD reference
Hi only here for the GD reference
@2:41 reminds me of a certain scene in the ending credits of the anime Charlotte.
I thought it looks cool being recreated using an equation.
How did you make it so smooth? It is beefy PC or you had to render some parts much slower and then speed it all up?
I love this and would have understood math so much more in school
Naw bro, those graphics are a whole bloodbath...
Frfr
LOL Bloodbath and Cataclysm!
Holy cow geometry dash song
Supersonic ?
@@maces1 At the speed of light
@@Brokeboy8579 BLOODBATH !!
@@Brokeboy8579 im so stupid
@@maces1 lol its ok
wow, i additionally love how this goes. with basic variables or position letter x and y, its used for graphs, code, and may types of stuff too!
its much more fun with the experience of advanced math and alot more :).
Increíble, como es posible que la matemática pueda hacer eso, algo inimaginable, un saludo @Andrew
i hear the beginning of "at the speed of light" and the only thing in my mind is geometry dash. it has locked itself in and is refusing to let me process any other thoughts
it's like a sleeper agent or something
Really cool, bravo!. You could also do a 3D version using GeoGebra, it probably would look great too, z=sin((√x²+y²)+a) looks like waves on water.
What I love about x^a is imagining thr curve on the negative side whizzing in circles and popping into existence again when it hits the real plane lol
0:16 the timing with the music god dang!
hearing speed of light immediately triggered fear
As a both Geometry and Geometry Dash lover I can say it is extreme calculus demon
i love that when you add tangent to something it always messes it up
Damn this level looks like an Extreme demon
Im ginding bloodbath right now and i unironically tense up when i hear the michigun part
this song brings me way back, but these are harder than the demons on geometry dash :))
didn't expect you going to use speed of light as a background song, literally sang the beat from the start of the video till the end
1:31 that one just hit me like a truck. I was not expecting that
1:15 I can see a sine wave moving through space and this would be the slope at x=0
1:30 This one is like cutting a cone with a plane at different angles and seeing what would be left in the plane
Damn, those two are really beautiful to observe
1:14 bloodlust played
The video: math
The music 🩸🛁
The song is called "At The Speed Of Light".
thank mr obvious
Im not mr obvious
@@вевекекс bruh
an awesome superpower would be to summon projectiles like this should you have the equation in your mind, or even create objects out of it.
This video gives 2010 vibes. Loved it!
do "y ≥ sinax + asinx + cosay + acosy" and zoom in really close to one of the blob edges
I like the fact that he used "at the speed of light" for a math vid