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I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown bellow:

4 dimensional plot 1

However, my $X$, $Y$, and $Z$ co-ordinates make up a $3$-dimensional meshgrid, so when I do the $4$ dimensional plot it is hard to see what is going on, as shown below:

4 dimensional plot 2

$X$, $Y$ and $Z$ represent spatial dimensions and $C$ represents a value that depends on its place its $3$-dimensional space. I need $X$, $Y$, and $Z$ to be shown in all places because these are the independent variables. In this simplified version of my function, $C=X+Y+Z$. I want to be able to pick any $3$ numbers for $X$, $Y$, and $Z$, and then look at my graph, and be able to get a good idea of what $C$ is. You can sort of do this with this current graph but it is hard to use.

What I want to know is: Is there a better way to plot this information? For example, is there a different co-ordinate system I could use that would be better? Or is there a way I could represent the 3 spatial dimensions so they look like a curved surface, but still include every point?

To reiterate that last question: Is there a way to represent every point in $3$ dimensions within $0 \leq X,Y,Z \leq 10$, all on one surface?


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And to think that I already had trouble with a $3$-dimensional plot... (which I solved with a $2$-dimensional plot with colors). But seriously, I don't think there's a simple way to do what you want. – TMM Mar 7 '14 at 20:10
If you are not restricted to static images, you could make a dynamic plot that you can move around, to see depth in your image. But if you want to put it in a paper or something, that wouldn't work. – TMM Mar 7 '14 at 20:12
(You might also want to try if you happen to be making such plots in Mathematica. Maybe they have some good suggestions.) – TMM Mar 7 '14 at 20:13
I'm not restricted to static images, the graphs shown can be moved around, however even with this, it is still hard (but not impossible) to get a good estimate of C just by looking at the x, y and z position. – Blue7 Mar 7 '14 at 20:14
I suppose it is fine to post it on as well. Perhaps you could slightly rephrase it to emphasize that (on that website at least) you are looking for visualization methods in Mathematica. By the way, some useful links: Visualizing 4D functions and 3D heatmaps. – TMM Mar 7 '14 at 20:21

You could try plotting the 3rd dimension with color and the 4th dimension with the saturation/brightness of that color?

share|cite|improve this answer
(Or more like tints and shades of that color) – Fred Jun 7 '14 at 18:48

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