This video is just... Perfect timing. Back to a year ago, i just found 'grape messy graph' video from japan from many many years ago. And this channel casually uploaded this video when i find more about it. Just perfect timing and i like it. Plus this video also included the equation suggested by your viewer.
I‘ve got some other heartshaped curves for you: 1. A sort of sine wave that forms into a heart for a parameter a increasing. Let a >= 0, y = x^(2/3)+0.9*sqrt(3.3-x^2)*sin(a*Pi*x) 2. Defines a group of curves together forming a heart (best shown if you draw with it with a trace). Let a be [1,20], (sin(a*Pi/10)+x)^2+(cos(a*Pi/10)+y)^2 = 1+0.7*|x|*y I hope I wrote it down correctly, if it doesn‘t work let me know! I would have some for 3D, but that‘s for another day…
Very cool. Here are some interesting complex number functions. You'll need GeoGebra or something similar since Desmos can't understand imaginary numbers. Lasers: sin(i*x) Repeating circles: i^x distorted grid: x^i I can't think of anything: i*tan(x) Diamonds: cot(tan(sin(i/x))) Concatenated cardioid curves: sin(i*cos(i/x)) Chaos: sin(i^cos(x))
i just stumbled across this, i’m so glad this exists! i used to do this stuff back in high school math class for fun! also i figured out how to make diagonal parabolas back then but i don’t remember how anymore, unfortunately, i would’ve loved to share
You are mostly correct. Here's one way to see this rigorously: If you perform the substitution u = x - y, the equation becomes u^3 = u + 2y y = (u^3 - u)/2, which does not have an asymptote along the line u=0, which would be the asymptote y=x in the original equation.
5:41 actually looks like this. I mean, the radius diverges more and more often as θ increases, so it eventually fills the plane if your graph-drawing pen has non-zero thickness.
The nice thing about `mod(x, m) < mod(y, m)` is that it's faster to compute than `sin(x) < cos(x)` but the pattern is not exactly the same, and you can control the size by changing the argument `m`. The `x^3 - xxx = 0` is probably due to floating-point rounding errors
6:13 i think it looks this way because theres e^x in the equation so above ~800 it exceeds the integer limit so cant show, in reality the graph would go on forever
you've got to zoom out pretty far for the effect to be apparent,. but r*theta = sin(theta^3) / cos(theta^3) is kinda interesting. as you zoom out, the spikes start to disappear tan(y) = -sin(x)^x makes seagulls (in +ve x anyway) y = sin(x^y) / sin(y^x) looks like rain on a lake
Saw all of the videos in these series and it inspired me to do some tries with Desmos, there are the two I liked the most: x^cosy = y^cosx and x(cosy^3)+y(cosx^3) =1 first one forms a really interesting waffle shape and the second one is just a mess!
I was tripping seeing the graphics and then... Opeth. Love that band man, and love people who loves that band. Here is my like for the video itself, and for your good taste
When I was messing around with the trigonometry functions on a graphing calculator, I found an equation that forms a very cool looking graph. Equation: sqrt(cos(2x * pi^2 * sin(y^2))) = pi^2 * y^2/x
my favourite is still sin^2(xy) = tan(xy), it is a repeating one as well and to get the most of it you have to scroll out a bit as well as to the side, the center is kinda boring sin^2(xy)=x^2e^-y^2 is also interesting, to make it single just take the square away of the y tan(y) = sin (x^2 y) as well - as it is mirrored on both axes it is kind of satisfying tan^2(y^2) = sin(xy) since people seem to like those bubbles edit: i just found some art tho, r = a + 2a * (cos(b*theta)+sin(b*theta)) a ={IR}, b = [1, 2] this makes clover leaves. i didnt find a formula to get any prediction on how many you get some are even appearing multiple times 1 leave b = 1 2 leaves b = 2 3 leaves b = 1.5 4 leaves b = 1.3 3 periodic 5 leaves b = 1.6 6 periodic 5 leaves b = 1.25 6 leaves b = 1.2 7 leaves b = 1.16 6 periodic 7 leaves b = 1.4 7 leaves b = 1.75 8 leaves b = 1.6 9 leaves b = 1.8 11 leaves b = 1.83 3 periodic actually i think thats all of the bs there is
yeah iirc you can make petal shaped flowers in polar with r = a + bcos(theta) or sin(theta) and the right ratio of coefficients of a to b. I don't remember off the top of my head but you can also make other shapes like limacons.
Next time you do one of these, try r=sqrt(theta). It's a normal spiral where each rotation get's closer and closer to the previous rotation. Also try increasing the upper limit. Do to Desmos' inaccuracy, it gets more and more angular as the upper limit increases. After 2500 is when the spiral starts to get angular, and at 100000 it becomes a really nice trianglular shape.
also, try (y^(x/y))/(x^(x/y))=(x^(y/x))/(y^(y/x)). The equation itself look completly insane, but's it's completly normal a straight line. I also did the math, and it checks out. That equation is just an overcomplicated way to write y=x.
This is my favourite one, i came up with this for fun. sum (bound very large ~100, n=1) of ((1/n^2)(cos(n^2 x))) as the boubd approaches infinity you get a non differentiable function symilar to the weistrass fxn
I was messing around with a graph I made that counts in binary mod(x, 2^floor(y+1)) > 2^floor(y) However, removing the floor functions produces some really stunning results. You can also swap out the ">" sign with a "=" sign and it will retain its stunningness
variable and trig spam is fun with this Yamsox's base triangle equation: x^{2}+y^{2}=\sec^{2}\left(\operatorname{mod}\left(\arctan\left(y,x ight),\frac{2\pi}{n} ight)-\frac{\pi}{n} ight)
Got one I remember doing with my own messing around. sin(cos(tan(xy))) = sin(cos(tan(x))) + sin(cos(tan(y))) Rather broken but kinda pretty near the center. I think anyway.
I suggest 2 formulas in desmos terms: \gcd\left(x,y ight)=1 in human terms: gcd(x,y)=1 in desmos terms: \gcd\left(\operatorname{mod}\left(x,a ight),\operatorname{mod}\left(x,b ight) ight) in human terms: gcd(mod(x,a),mod(x,b)) depending on variables a and b.
i was preparing for my math test and watching some lessons on TH-cam and for some reason it recommended me this video its not like im complaining though
Very cool videos, all of 3 episodes. If you search for a funny spiral, tan( (x^2 + y^2)^(-1) ) = y/x. Otherwise, you can print a Mandelbrot set in Desmos: define f(z) = (z.x^2 - z.y^2 + x, 2z.xz.y + y) ; define D(z) = sqrt(z.x^2 + z.y^2) ; graph D(f(f(....f(f(((x,y))))....))) . IMPORTANT: keep 3 pair of parenthesis after last f, and the right dot or comma in the functions! More f you put, more precise Mandelbrot set is
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff is it more precise now? edit: wow it is
If you’re still doing these I’ve found quite a few interesting graphs: cosx^2+cosy^2=cosxy (or tangent/ without the squares) sin((6+x^3)/xy)=cosy (Beautiful center, sides are madness) x^n= siny (repeated squares) y+x= abs(tany) x^30+y=tany (Beakers) sin(|x|+|y|)=cosy
Desmos doesn't actually like Q3 the most, the bottom left of the screen just contains some form of rendering glitch/error/etc. In fact, if you move the graph around, the clump of more concentrated mess will remain in almost exactly the same place on the screen, so long as there is sufficient mess for it to be rendered.
These have been interesting to put into my marching pixels (marching squares, but each square is a pixel) algorithm - Most of them are the same, though due to how the marching squares algorithm works there's no such thing as a non-enclosed shape so many of the graphs have lines connecting things that aren't connected in Desmos
The problem isn't in maths. x^3 - x*x*x = 0 -> 0 = 0, the whole number plane is the answer to it. Desmos represents it wrong though - instead of coloring the entire plane, it does... that.
This reminds me of getting bored and playing around with random functions in precalc class until I found something cool
122 likes and no replies? Lemme fix that
Is that pfp an interrobang? :O
Whenever my math teacher gives us something to do on desmos I do that too
i do that all the time
‽
This video is just... Perfect timing. Back to a year ago, i just found 'grape messy graph' video from japan from many many years ago. And this channel casually uploaded this video when i find more about it. Just perfect timing and i like it. Plus this video also included the equation suggested by your viewer.
So what
@@Andrewman That's really cool! Both of your channels are incredibly satisfying.
Glad to see there's a math equation for my stress graphs
I‘ve got some other heartshaped curves for you:
1. A sort of sine wave that forms into a heart for a parameter a increasing. Let a >= 0, y = x^(2/3)+0.9*sqrt(3.3-x^2)*sin(a*Pi*x)
2. Defines a group of curves together forming a heart (best shown if you draw with it with a trace). Let a be [1,20], (sin(a*Pi/10)+x)^2+(cos(a*Pi/10)+y)^2 = 1+0.7*|x|*y
I hope I wrote it down correctly, if it doesn‘t work let me know! I would have some for 3D, but that‘s for another day…
What about x² - |x|y + y² ≤ 1
thats what it looks like in my eyes :/
@@nidhiagrawal3354 That‘s a simple but pretty one, I like it!
There's also (x² + y² - 1)³ - 3x² × y³ ≤ 0, definitely my favorite heart graph.
A=(10^11)+10^3
Therapist : Desmos hamburger face isn't real, it can't hurt you.
Desmos hamburger face : 4:57
First part: 1 year ago
Second part: JUST YESTERDAY
Very cool.
Here are some interesting complex number functions. You'll need GeoGebra or something similar since Desmos can't understand imaginary numbers.
Lasers: sin(i*x)
Repeating circles: i^x
distorted grid: x^i
I can't think of anything: i*tan(x)
Diamonds: cot(tan(sin(i/x)))
Concatenated cardioid curves: sin(i*cos(i/x))
Chaos: sin(i^cos(x))
x^i^i^x = crash
x^i*i^x = an infinite quasar
i * tan(x) looks like a magnetic field
0:50 danicker
3:10 audigamer
6:17 the farlands in minecraft
fr
6:30 - that you see if you look down from any tower in NYC
some of my trig experimentation:
x^2 - y^2 = csc(xy)
sin(x) - sin(y) = (x/y)
sin(|x|) = cos(xy)
sin(x^2) = sin(y^2)
x^2 = sin(xy)
sec(x) >= sec(y-pi)
i just stumbled across this, i’m so glad this exists! i used to do this stuff back in high school math class for fun!
also i figured out how to make diagonal parabolas back then but i don’t remember how anymore, unfortunately, i would’ve loved to share
Iirc blackpenredpen made a video on rotating parabolas
Tiger
Add an xy term
1:16 I don't think y = x is an asymptote. This graph is just a stretching and rotation of y = x^3.
You are mostly correct. Here's one way to see this rigorously:
If you perform the substitution u = x - y, the equation becomes
u^3 = u + 2y
y = (u^3 - u)/2,
which does not have an asymptote along the line u=0, which would be the asymptote y=x in the original equation.
5:41 actually looks like this. I mean, the radius diverges more and more often as θ increases, so it eventually fills the plane if your graph-drawing pen has non-zero thickness.
I have a suggestion!
Sunlight year chart for the northern hemisphere (where x is the day of the year & y is the hour of the day)
Equation: y
Note: This equation only works for degrees.
What? Keep it going, these are great graphs
It's amazing what an equation can do. I wonder if there's an equation that draws my face.
have you ever heard of bezier curves?
Probably a piecewise one
Depends on what is "your face"
The nice thing about `mod(x, m) < mod(y, m)` is that it's faster to compute than `sin(x) < cos(x)` but the pattern is not exactly the same, and you can control the size by changing the argument `m`.
The `x^3 - xxx = 0` is probably due to floating-point rounding errors
Hi andrew, i think i have found an interesting graph, although it is a bit complex:
y=lcm( sin(x), lcm( x^y, sin(y^x)))
pretty cool thunder
what does it look like tho
Really awesome series. I hope you keep making more.
Can someone explain why at 4:17 x^2 is in module? is it in case of complex numbers?
i also dont know but its not complex numbers because those graphs uses only real numbers x and y
in fact this is nonsense, literally any number possible will never have a negative square
1:50 I feel like the graph for (x^3)-(x*x*x)=0 is a computer science lesson in floating point numbers. Any time that y!=0 is a rounding error.
sin(xy)=e^(xy) is funky squares
tan(x/y)=x is kind of a basketball
sin(y)+x=e^y - x^2 is dripping stuff
6:13 i think it looks this way because theres e^x in the equation so above ~800 it exceeds the integer limit so cant show, in reality the graph would go on forever
you've got to zoom out pretty far for the effect to be apparent,. but r*theta = sin(theta^3) / cos(theta^3) is kinda interesting. as you zoom out, the spikes start to disappear
tan(y) = -sin(x)^x makes seagulls (in +ve x anyway)
y = sin(x^y) / sin(y^x) looks like rain on a lake
It get's even more interesting if you zoom in instead. It goes from stars in the sky to spiderweb
for the last one, you can use log{y}x = tan(xy), which makes it look close enough, with finer detail
the periodics functions are visualy really good, this channel is very interesting
Please don't stop doing this videos!!!
This was such an amazing one of a kind series!
Saw all of the videos in these series and it inspired me to do some tries with Desmos, there are the two I liked the most:
x^cosy = y^cosx
and
x(cosy^3)+y(cosx^3) =1
first one forms a really interesting waffle shape and the second one is just a mess!
Omg I love your content! Keep doing this cool math thing
I was tripping seeing the graphics and then... Opeth. Love that band man, and love people who loves that band. Here is my like for the video itself, and for your good taste
At 6:10, the graph that creates really reminds me of the Minecraft farlands.
Hi Andrew, loving the videos. Could you tell us the names of the songs you're using? Especially the first one! Thanks so much :)
I think it's so weird when the equations and expressions generate an asymmetrical visualization.
Nice, my graph got there :) The hamburger generator was really creative.
Damn i love these graph videos.
Even though i have no idea how any of this math works.
5:44 doesn't have any inacuracies. If θ goes to infinity, the entire screen should fill.
2:26 looks a little bit like 🙋♂️🇩🇪
🇩🇪🇮🇹🇯🇵
art school man
5:42 anime lines green screen function.
amazing and useful!
I want to hear the funny sounds that come with the graphs
0:50 the graphs in cursed desmos sounds be like:
Not first!
P.S. You should try plotting in Maxima!
for x^3 - xxx = 0... Maybe it goes like this because of floating-point arithmetic?
And maybe many other graphs too
try x^2 = y^(50sin(x)sin(xln(y))) scale from -20 to 20
This equation contains fine detail that has not been fully resolved.
When I was messing around with the trigonometry functions on a graphing calculator, I found an equation that forms a very cool looking graph.
Equation: sqrt(cos(2x * pi^2 * sin(y^2))) = pi^2 * y^2/x
Damn this music goes hard. Love the combination!
warning: This video contains graphic content
my favourite is still sin^2(xy) = tan(xy), it is a repeating one as well and to get the most of it you have to scroll out a bit as well as to the side, the center is kinda boring
sin^2(xy)=x^2e^-y^2 is also interesting, to make it single just take the square away of the y
tan(y) = sin (x^2 y) as well - as it is mirrored on both axes it is kind of satisfying
tan^2(y^2) = sin(xy) since people seem to like those bubbles
edit: i just found some art tho,
r = a + 2a * (cos(b*theta)+sin(b*theta)) a ={IR}, b = [1, 2]
this makes clover leaves. i didnt find a formula to get any prediction on how many you get
some are even appearing multiple times
1 leave b = 1
2 leaves b = 2
3 leaves b = 1.5
4 leaves b = 1.3 3 periodic
5 leaves b = 1.6 6 periodic
5 leaves b = 1.25
6 leaves b = 1.2
7 leaves b = 1.16 6 periodic
7 leaves b = 1.4
7 leaves b = 1.75
8 leaves b = 1.6
9 leaves b = 1.8
11 leaves b = 1.83 3 periodic
actually i think thats all of the bs there is
more bubbles
log(cos(ye!))=tan(sin(xπ!))
yeah iirc you can make petal shaped flowers in polar with r = a + bcos(theta) or sin(theta) and the right ratio of coefficients of a to b. I don't remember off the top of my head but you can also make other shapes like limacons.
MORE about math graphs, I like it
its amazing how trig functions together can make such fascinating graphs. cos xy = sin(tan yx)
5:36 Geogebra seems to show this graph pretty well, and I can confirm it's a nice graph
6:14 reminds me of the Minecraft Farlands so much!!
a = coth(y! * x) + 1 / a > 1
lower axis gave some funky inverted spike graph.
Next time you do one of these, try r=sqrt(theta). It's a normal spiral where each rotation get's closer and closer to the previous rotation. Also try increasing the upper limit. Do to Desmos' inaccuracy, it gets more and more angular as the upper limit increases. After 2500 is when the spiral starts to get angular, and at 100000 it becomes a really nice trianglular shape.
also, try (y^(x/y))/(x^(x/y))=(x^(y/x))/(y^(y/x)). The equation itself look completly insane, but's it's completly normal a straight line. I also did the math, and it checks out. That equation is just an overcomplicated way to write y=x.
@@thatoriginalguy6213actually it's y=x [x≥0]
This is my favourite one, i came up with this for fun.
sum (bound very large ~100, n=1) of ((1/n^2)(cos(n^2 x))) as the boubd approaches infinity you get a non differentiable function symilar to the weistrass fxn
You can zoom in very far and it is almost self similar
Another one: Take the Riemann Zeta function and replace Zeta(s) with r, s with thêta and infinity with k.
Then you can try to tweak those numbers
Suits perfectly with the moment, i am studying functions and this is cool, even if i don't understand sin(e)^x and stuff like this lol
6:19 Minecraft farlands
I was messing around with a graph I made that counts in binary
mod(x, 2^floor(y+1)) > 2^floor(y)
However, removing the floor functions produces some really stunning results. You can also swap out the ">" sign with a "=" sign and it will retain its stunningness
5:39 is the green screen they put on fast running scenes in anime
How you take factorial with a negative argument? Is it Gamma-function? (Sorry for my English)
yes
I twould be cool for the ones where desmos crashed and burns if you could give an approximation of what the graph would actually look like.
I used to play around with random functions on desmos
sin(x^4)^y=100 - looks like raindrops falling when you're zooming in/out
0:37 Eren Yeager function
variable and trig spam is fun with this Yamsox's base triangle equation: x^{2}+y^{2}=\sec^{2}\left(\operatorname{mod}\left(\arctan\left(y,x
ight),\frac{2\pi}{n}
ight)-\frac{\pi}{n}
ight)
Got one I remember doing with my own messing around.
sin(cos(tan(xy))) = sin(cos(tan(x))) + sin(cos(tan(y)))
Rather broken but kinda pretty near the center. I think anyway.
The thumbnail is my graph suggestion, nice
0:55 my heart rate when something creaks at night
imo csc is the most chaotic trig function
something like :
y=csc(xy)
sqrt(nx+y)
*Beautiful!*
I suggest 2 formulas
in desmos terms:
\gcd\left(x,y
ight)=1
in human terms:
gcd(x,y)=1
in desmos terms:
\gcd\left(\operatorname{mod}\left(x,a
ight),\operatorname{mod}\left(x,b
ight)
ight)
in human terms:
gcd(mod(x,a),mod(x,b)) depending on variables a and b.
Desmos "why this guy hates me so much" 😂😂
Are there more accurate graph plotters than desmos?
My favorite is r = θ×0.05
0≤θ≥10000
Zooming out makes it look like a galaxy
i was preparing for my math test and watching some lessons on TH-cam and for some reason it recommended me this video
its not like im complaining though
Not seeing this should be a crime.
Very cool videos, all of 3 episodes. If you search for a funny spiral, tan( (x^2 + y^2)^(-1) ) = y/x. Otherwise, you can print a Mandelbrot set in Desmos: define f(z) = (z.x^2 - z.y^2 + x, 2z.xz.y + y) ; define D(z) = sqrt(z.x^2 + z.y^2) ; graph D(f(f(....f(f(((x,y))))....))) . IMPORTANT: keep 3 pair of parenthesis after last f, and the right dot or comma in the functions! More f you put, more precise Mandelbrot set is
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
is it more precise now?
edit: wow it is
If you’re still doing these I’ve found quite a few interesting graphs:
cosx^2+cosy^2=cosxy (or tangent/ without the squares)
sin((6+x^3)/xy)=cosy (Beautiful center, sides are madness)
x^n= siny (repeated squares)
y+x= abs(tany)
x^30+y=tany (Beakers)
sin(|x|+|y|)=cosy
I remember this music from a video " Can ____ trojan" destroy windows xp" or something like taht
Desmos doesn't actually like Q3 the most, the bottom left of the screen just contains some form of rendering glitch/error/etc. In fact, if you move the graph around, the clump of more concentrated mess will remain in almost exactly the same place on the screen, so long as there is sufficient mess for it to be rendered.
These have been interesting to put into my marching pixels (marching squares, but each square is a pixel) algorithm - Most of them are the same, though due to how the marching squares algorithm works there's no such thing as a non-enclosed shape so many of the graphs have lines connecting things that aren't connected in Desmos
Some cool textiles pattern: (sinx)^-3
What's the difference in Desmos between x^3 and x*x*x?
finally, something to do when i'm bored in class
I wouldn't call 3:52 trypophobia as the holes are arranged on a grid. Trypophobia is triggered by irregular arrangements of holes
I agree
1:51 this is very strange to me. Can someone explain why this happens? I‘ve taken up to college algebra
The problem isn't in maths. x^3 - x*x*x = 0 -> 0 = 0, the whole number plane is the answer to it. Desmos represents it wrong though - instead of coloring the entire plane, it does... that.
1:07 love does exist in math.🥰
Yes it does but never long. You need an account for that
Bro was just looking to see the crazy graphs people have discovered and OPETH COMES ON?? What a nice surprise!
Glad you’re into calculus as well ^_^
y=gcd(tan x,cot x,sin x,csc) is a wierd ladder thingy and tan((y+0.5)!)=sec(x!)is like the tangent of a circle but cursed
x^3 - xxx = 0 is only buggy because the graph applies everywhere.
2:13, greate! but you need one more bracket...
everything gets so silly with theta, even r=sin(theta^2) is fun
More graphs))) thank you!
0'58 This graph is discontinuous.
If this is math a few years later I am going to die
Oh. Desmos doesnt like those? You know what time it is then? Its scratch time!
One of my friends showed me once: sqrt(x^2)+0.9(sqrt(3.3-(x)^2)*sin(10pix)
everybody gangsta until the asian kid solves an equations that shows enchanting table language on the graph