Post cool function graphs
isn't that squeeze theorem
watching this thread
>>8051231
its that and x^2 sin(1/x)
>>8051229
>>8051276
>reading about the definition of the function
How do people como up with this shit? Fucking changing bases and shit man
Thomae's function.
Continuous at every irrational, discontinuous at every rational.
>>8051400
If something like the Cantor function doesn't spring to mind as soon as you see the Cantor set and definition of continuity, math probably isn't the field for you.
>>8051421
:^)
>>8051421
>I've seen the definition, therefore I could have easily come up with it
sure buddy, you probably would have come up with the weierstrass function aswell right?
>>8051419
at least post a pic
>>8051254
>>8051462
>he thinks it's hard to come up with
brainlets
>>8051524
fucking around with circles is fun
>>8051254
What's the full equation? it's cut off.
i like how none of this is symmetrical
>>8051243
this is one of those function that is still noisy no matter how much we focus
so we can zoom in arbitrarily close
but what if we zoom into the planck length? would it still look like that?
>>8053141
are you asking if numbers can be quantized?
it would look the same
>>8053141
It would look the same. There's no limitation to how far you can zoom in.
>>8053141
>what if we zoom into the planck length?
You're talking about some arbitrary physical length in regards to a distance on a graph, this makes no sense.
Graphs of abstract functions aren't measured in metres, just numbers.
>>8053141
Tell ne if I am mistaken. The plank length is a physical limitation, whereas in mathematics there is no real limit.
>>8053141
you don't seem to understand the concept of the real numbers, or what the planck length is
why do you even visit /sci/?
>>8053978
wolfram alpha and desmos
>>8053141
Please, PLEASE be bait.
>>8053141
Yes but you need to prove the Riemann Conjecture for that.
>>8054324
>honest question about something he did not understand
>no snark, no sarcasm
>hoped /sci/ would answer it, or give links to where he could read up
>gets this response instead
fuck off, bully
>>8054618
Only a fundamentally retarded bait-level anon can ask about Planck length outside of physics.
>>8054235
It isn't a limitation, it's just a unit of distance derived from fundamental constants. It's in the area of what we reckon is the smallest measurable length but it's not related to that.
It's real significance is that it is the length scale at which a quantum theory of gravity would be required.
>>8055491
*its
>>8055800
It's a fine question, but it tells us the asker is retarded. I won't fault the question for being itself.
>>8051229
>>8056034
>piecewise
1/10
>>8056061
this
>>8055800
It's not a good question, "zooming into the Planck Length" on a graph makes no sense
>>8056034
Make it into one equation and I'll be impressed.
>>8056415
Who is this cutie
>>8056211
I tried
>>8051276
Never saw this before. Interesting function
Gotta love'em chaotic systems.
>>8056627
Noone thought of this?
>>8051237
Fourier Series.. My nigga.
>>8056935
nobody has thought of that Carlos
Tupper's Self-Referential Formula
>>8051244
i had fun figuring that out
this fine detail shit is fuckin rad
>>8057029
I would pay money if this app can offload the calculation to my local machine to get more detailed graphs.
>>8056957
You can't prove a definition.
>>8056980
>literally just makes every possible combination
>>8056922
[math] f\left( x,y \right)\; =\; -\frac{M_{0}}{\left( \left( x-r_{0} \right)^{2}+y^{2} \right)^{\frac{3}{2}}}\left[ \begin{array}{c} x-r_{0} \\ y \end{array} \right]-\frac{M_{1}}{\left( \left( x-r_{1} \right)^{2}+y^{2} \right)^{\frac{3}{2}}}\left[ \begin{array}{c} x-r_{1} \\ y \end{array} \right] [/math]
[math] \frac{d^{2}}{dt^{2}}\left[ \begin{array}{c} x \\ y \end{array} \right]=f\left( x,\; y \right),\; \frac{d}{dt}\left[ \begin{array}{c} x \\ y \end{array} \right]=v_{0},\; \left[ \begin{array}{c} x \\ y \end{array} \right]=p_{0},\; t=0...2000 [/math]
Unfortunately, it doesn't account for the motion of the two massive objects, meaning no Lagrange points. I am still trying to do that.
>>8057098
Beautiful
>>8057014
What software?
>>8056573
>parametric
get out
I want a function whose graph is its own symbolic expression.
For example, if the graph of [math]y = x^2[/math] visually looked like [math] y = x^2 [/math].
>>8056569
Circles in a finite field (F_431 I think), a friend and I were thinking of what we could say about geometry on finite fields a while ago but we didn't find time to get into it
>>8057413
Completely impossible.
>>8057495
There are computer programs that output their own syntax. So I wouldn't dismiss it so outright.
>>8056657
Lel it's real.
I went on wolfram and found a curve that looks like spongebob and wolfram gave me the formula to it, but it's hundreds and hundreds of lines long.
How does Wolfram calculate something like that? How does it know how to do that?
>>8056573
The trick is to divide over the parts you don't want in the range you don't want them.
We had to make the batman equation you gave above into one equation in my high school precalc class years ago but I have absolutely no memory of how to do it.
>>8057508
It wouldn't be a function if it had the property he describes.
>>8057119
Sorry to be so technical but...isn't that not a definition? It's an axiom of ZFC, yes?
>>8057535
Good point.
What if he had said a relation in R^2 instead?
Is there a good reason why that would be impossible?
>>8057544
Yes, but it's not a function. I was being pedantic, but still
>>8057573
No I realize you're right. It frustrates me when professors and sometimes textbooks neglect the distinction.
>>8051607
that's just a plotting artifact.
>>8057098
Just get something like WinPlot or Maxima or pirate something like Mathematica
>>8057517
Someone creates it and saves it. Simple shapes are easy to figure out in parametric form, you can also use something like Mathematica's "manipulate" or Desmos' "tremendous faggotry" to create a general form of a piece you want and screw around from there.
>>8057536
It's not an axiom of ZFC.
>>8057517
Get an image
Apply edge detection and shit, get a bunch of lines.
Delete lines you don't need.
Use some sort of automatic line curve equation generator.
??????
PROFIT
How do I reflect [math]y = x^{x}[/math] about the y-axis m8s
I need to use complex numbers right
>>8057703
https://www.wolframalpha.com/input/?i=Solve+1+%3D+-%7Cx%7C%5E-%7Cx%7C
Well shit. Would complex numbers even work?
Someone should answer this for him.
>>8057703
(-x)^(-x)
y3 was -(x^(-x))
>>8057731
x^x = -x^-x can only have the solution x=iPi/2ProductLog(iPi/2)
>>8057703
Here
>>8057222
https://www.desmos.com/
Enjoy, fampai.
>>8057761
That's not the question though.
The question is for what values of x, either real or complex, can |-x|^|-x| be a positive real number?
For example, what value of x satisfies |-x|^|-x|?
He is asking about flipping over the y-axis, not the x-axis.
>>8057797
Well what is it? What value of x, either real or complex above will result in a positive real number?
The complex numbers are closed under exponentiation.
So there should be a solution to -|x|^(-|x|) = 1.
What is the solution?
>>8057862
I'm also quite interested in the minimum point on the [math]y = x ^{x}[/math] graph, which looks to be around x = 0.36... and either lower or higher values always give you a higher y-value. I know I'm quite a math noob but it seems like this point is probably significant in some way outside of the x^x curve and may have some weird properties, although I'm really not sure. It's just interesting to me that you put in something seemingly quite abstract like x^x and get out a very real definite, yet probably irrational number.
>>8057600
I disagree
>>8057098
here it is in derive, dont know if it can get much better than this.
>>8058205
Here's a much better version. Took a couple minutes, I could leave it running overnight for near-flawlessness. I'd worry I can't get much better before image compression starts to screw things up though.
As expected, most of the cool roughness goes away with precision.
>>8058263
amazing
>>8058263
ALL
NIGHT
LONG
>>8057858
Jesus christ this is the shit
>>8056034
>>8058351
You should get a real CAS with real plotting software. Desmos is just a quick tool for middle school teachers.
>>8058263
damn thats pretty cool anon
what'd you use to make this?
>>8057098
Here's Mathematica's plot.
>>8056958
i feel like those axes should be swapped
>>8060325
what sorcery is this
>>8057029
here is the same relation using GrafEq
My favorite """function"""
>>8062231
it's a curve
>>8062215
another interesting graph from GrafEq
>itt """""""""""functions"""""""""""""
made this years ago with geobra
fav
>>8057098
Just learn computer graphics and shader code dumbass. Don't pay for a thing that takes literally 5 minutes to code.
>>8062231
product log is pretty useful desu
This thread seems a good a place as any to ask this.
Can somebody recommend me a program/website for graphing multivariable functions, two functions to one graph? Bonus points for cheap/free and GUI (have used matlab in the past but don't have time revising that right now).
>>8065556
Holy shit man, apply yourself.
Mathematika, desmos, wolframalpha
>>8065556
SageMathCloud can probably do this
>>8065599
Actually, not GUI enough. It looks great, but all I want is something to geometrically explore functions subject to constraints of other functions for these Lagrange multiplier problems I'm working on this week, without having to learn any code.
Anyone else?
>>8065614
mathway.com/graph
>>8065616
>multivariable
>two functions to one graph
or am I being retarded?
>>8051229
Why do people use [math]x^2 \sin{\frac{1}{x} }[/math] to demonstrate the squeeze theorem? [math]x \sin{\frac{1}{x} }[/math] should be enough desu.
>>8056657
never noticed this could be done
>>8066337
idk ask spivak i got it from him
>>8066337
doesn't look as cool
>>8065602
Implying you cant use mathematika for multivariable. Implying you cant use wolframalpha for almost any mathematika code line if you know how.
Implying you cant plot different equations in the same graph on desmos and all of them.
What?
>>8057132
that's the beauty of it
>>8051254
Desmos is pretty cool
