Should I use 2D or 3D graphs for Implicit Functions?

[DrummingAtom]

I've began learning some Implicit Functions but graphing them seems to be a problem. I'm using MathGV for graphing. Should I choose 2D or 3D graphs? It's not graphing with 2D, and solving for x or y would be an even bigger problem.

For instance, 3(x^2+y^2)^2 = 100xy will graph in 3D but is this really a 3D function?

Thanks.

 

[Tac-Tics]

For instance, 3(x^2+y^2)^2 = 100xy will graph in 3D but is this really a 3D function?

There is no such thing as a "3D function" or a "2D function". Functions are functions. They are maps. They take input values and produce output values. Sometimes those input and output values are real numbers. Sometimes they are points in space. But we don't call them 3D or 2D functions.

Implicit functions aren't really functions. They are bastardizations. More technically, they would be called relations. You can think of it as a statement of two variables (x and y) which can be either true or false (the equation is satisfied or not).

Since your equation has two variables, its graph is a collection of points in the plane. I'm not familiar with the particular software you're using, but it's often a pain to graph equations like this, because it's simply harder (computationally speaking) to graph than a function. You have to iterate over every pixel, take its coordinates as x and y, and then evaluated the expression. If the expression is true, you plot the point. Otherwise, you leave it blank.

 

[gammamcc]

Maybe try 2d but in polar...
Looks like cartesian coords needs y=function of x
noting samples on http://www.mathgv.com/