TITLE: Visualizing functions with a number of independent variables
QUESTION [7 upvotes]: I need to graph real valued functions (for exposition and analysis).
The issue is: there are more independent variables so that the conventional graphing methods can't be used, and furthermore I don't want to slice the functions.

These functions are like $s=f_1(x,y,z,t)$ and $s=f_2(x,y,z,t,k)$
I also have vector functions of the same type: v = g1 (x,y,z,t) and v = g2 (x,y,z,t,k)

The motivation is to see the functions intuitively at one go and maybe compare them. I know that there is a limitation of physical dimensions. Domain coloring has its own limits in this regard. My question is:

Do we have a visualization methodology for such requirements? 

It will be a benefit if one could refer to a software tool.
Any thoughts/suggestions are welcome.

REPLY [2 votes]: A tool for visualizing functions that is sometimes as powerful as graphs is using mapping diagrams. 
The simple idea is that each real variable is represented on an independent parallel axis in 3 space. One can place a point in space not on any axis to represent the function and arrows from points on the domain axes to the function point and arrows to points on the target axes corresponding to the values of the function for the domain points.
See Alfred Inselberg. Parallel Coordinates: Visual Multidimensional Geometry and Its Applications  (Springer, Oct 8, 2009) for more on multi-dimensionsal connections and http://users.humboldt.edu/flashman/MD/section-1.1VF.html for an (draft) introduction to visualizing functions of one variable with mapping diagrams.