# Cool 3-D functions for graphing

• LPHY
In summary: Graph: sin(xy-2) - cos(z) = 0In summary, users are discussing various equations and functions to use for a 3D graphing tool. Some examples include x*y^3-y*x^3, (x^2+3*y^2)*e^(-x^2-y^2), -x*y*e^(-x^2-y^2), -1/(x^2+y^2), cos(abs(x)+abs(y)), and cos(abs(x)+abs(y))*(abs(x)+abs(y)). They also mention the possibility of using implicitly defined functions. There is some discussion about a bug in the forums BBCode builder, but ultimately they are able to share links to their graphs,
LPHY
I am collecting nice 3-d functions to demonstrate graphing tool, if anyone have great functions which will look great on 3-d plotting, please let me know.

Here are few equations I am using now. If you guys need I can provide a link to plot each of these graphs.

(01) x*y^3-y*x^3
(02) (x^2+3*y^2)*e^(-x^2-y^2)
(03) -x*y*e^(-x^2-y^2)
(04) -1/(x^2+y^2)
(05) cos(abs(x)+abs(y))
(06) cos(abs(x)+abs(y))*(abs(x)+abs(y))

Note:
I have discuss some 2-D functions for my earlier tool, which you can see on this thread
Cool 2-D functions for graphing

You can probably find cooler functions if they're implicitly defined. Can your graphing tool handle those?

Office_Shredder said:
You can probably find cooler functions if they're implicitly defined. Can your graphing tool handle those?
I am not sure what you looking for, here is one sample 3D graph drawn from the tool
Graph: cos(abs(x)+abs(y))*(abs(x)+abs(y))

There was a bug, when some one put a function with spaces in middle, forums bbcode url not working, this is fixed now.

How come Arildno didn't suggest to plot f(x, y) = 0 yet..

How come Arildno didn't suggest to plot f(x, y) = 0 yet..
He is a lost case, so I resigned from trying to make him appreciate the beauty of the Great Annihilator.

I'll be back if he tries to top f(x,y,z)=0 in 4-D, though.

LPHY said:
I am not sure what you looking for, here is one sample 3D graph drawn from the tool
Graph: cos(abs(x)+abs(y))*(abs(x)+abs(y))

I mean, for example, if I said to graph cos(z) + sin(xy - 2) = 0, could it graph that for z as a function of x and y?

Office_Shredder said:
I mean, for example, if I said to graph cos(z) + sin(xy - 2) = 0, could it graph that for z as a function of x and y?

Sorry you cannot graph this function

cos(z) + sin(xy - 2) = 0

function must be in this format

f(x,y)

where

f(x,y) = z

1/(sin(abs(x)+x)-cos(abs(y)+y))

Last edited:
LPHY said:
Its look great, let me try the link again
Graph: (floor(-e^(-x*y/1)*cos( (x^2+y^2)/10 ))+14*ln(10000/(x^2+y^2)+.01))*floor( cos(x^2+y^2)/10)+3*(ceil(x)-floor(x))*(ceil(y)-floor(y))

You are right, some thing wrong with the built in forums bbcode builder, when I copy and paste the URL, it is working fine. Probably a bug, may have to work on that to fix it for long formulas.
floor(e^(abs(x*y/2))+round(1/cos(x*y))) works out just as well, and doesn't look nearly so ugly from a function point of view

Last edited:
When I came up with my first function above, I was goofing around with various functional forms. When I came upon something I liked, I used it and didn't reduce it to a visually-similar but functionally-simpler form.

robphy said:
When I came up with my first function above, I was goofing around with various functional forms. When I came upon something I liked, I used it and didn't reduce it to a visually-similar but functionally-simpler form.

I actually wasn't specifically trying to reduce your function, I just happened to stumble upon it (before looking at yours actually)

Did you change the program or something? Because 1/(sin(abs(x)+x)-cos(abs(y)+y)) is coming out differently now than it was before (specifically, part of it doesn't even show up)

Didn’t do any changes to the program, did you try adjusting the Z-Axis boundary limit.

Try and see whether its work for you, if you are not sure the range you can set it to

z-min = Auto
Z-max = Auto

Actually you can graph this...I tried it in grapher on my mac and it worked like a charm...

LPHY said:
Sorry you cannot graph this function

cos(z) + sin(xy - 2) = 0

function must be in this format

f(x,y)

where

f(x,y) = z
[QUOTE]Actually you can graph this because grapher works with it...

## 1. What are some common 3-D functions used for graphing?

Some common 3-D functions used for graphing include quadratic functions, cubic functions, exponential functions, trigonometric functions, and logarithmic functions.

## 2. How do I graph a 3-D function?

To graph a 3-D function, you will need to use a graphing calculator or graphing software. Input the function into the calculator or software and choose the 3-D graphing option. Adjust the viewing angle and scale as needed to get a clear visualization of the function.

## 3. Can 3-D functions be used to represent real-world data?

Yes, 3-D functions can be used to represent real-world data. For example, a quadratic function can be used to model the trajectory of a thrown object, and an exponential function can be used to model population growth.

## 4. What are some advantages of graphing 3-D functions?

Graphing 3-D functions allows for a visual representation of complex mathematical relationships, making it easier to understand and analyze the data. It also allows for the exploration of multiple variables and their interactions.

## 5. Are there any limitations to graphing 3-D functions?

One limitation of graphing 3-D functions is that it can be challenging to accurately represent the function in three dimensions. It also requires specialized tools such as graphing calculators or software, which may not be readily available to everyone.

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