Plotting functions of three variables What are some ways that people know to plot a function of three variables, in a way that is relatively easy to understand on paper?
Although this could be generalized to pretty much any scenario, I'm specifically looking at a process where I can control pressure, power, and temperature. My output is a single number. I'd be interested to know what kind of answers people come up with.
My closest attempt:
One could use a regular 3D plot, where two axes represent two of the three independent variables, and the third one represents the output. Then color can be used to indicate the third independent variable. But this plot gets cluttered with information, especially when the input space is sampled well.
 A: You could use a reactive 3D surface, with reactivity with respect to the value of the third variable. 
A: Use several linked graphs instead of a single graph.
Using the example from Stéphane Laurent's answer, which has 4 Xs and 1 Y (5Xs if you count the blocking variable). One way to view such high-dimensional models is with a Profile Plot, which is a series of linked 2D plots, where for each plot, one X varies and the others are fixed. (This example is specific the my product, JMP, but I hope the concept applies to whatever tools you have.)

The red dotted lines show the fixed value of each variable in the other plots. Clicking in a graph moves that X value as it applies to the other graphs. For instance, clicking on a low R value in the 2nd graph produces:

And clicking on a high R value produces:

The way the W graph has changed slope illustrates the negative interaction between R and W. Of course, that's also indicated by the significant R*W term of the regression model.
The dotted blue lines show the confidence intervals, which in this case are small enough to suggest good confidence in the model.
A: Ternary plots are one option. Stata command and example:

R solutions available too.
Alternative solution - contour plot. In Stata you would get:

Or using contourline: 

As you see, apart from easting and northing you can encode third variable (depth in example above) to color. Pretty sure R and other software would get you a graph like that too.
