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.


1. These functions are like $s=f\_1(x,y,z,t)$ and $s=f\_2(x,y,z,t,k)$
2. 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.



Visualizing functions with a number of independent variables
For time-dependent and three-dimensional data, there exist a number of established programs already; among the most popular free and open source ones are [Paraview](http://www.paraview.org/) and [VisIt](https://wci.llnl.gov/codes/visit). Both support a variety of plots such as isosurfaces, volume rendering or (for vector-valued data) arrow or streamline plots.


They all have a bit of a learning curve, though, and you should not expect to be able to see a four- or five-dimensional function on a two-dimensional screen "at a glance". 
Visualizing of and and data-mining from high-dimensional data are very active research topics in computational science, though. I would thus suggest thinking about *what kind* of information about your functions you would like to see about your functions, and then ask on the [Computational Science SE](https://scicomp.stackexchange.com/). (See for example this [question](https://scicomp.stackexchange.com/questions/1433/tools-for-visualizing-large-3d-volumes).) 


