How can I represent and visualize my four dimensional system in a meaningful way?

I currently have a plot where there are three dimensions plotted and a fourth variable is represented by color. Regions with the same color represent areas where the fourth variable is close to equal. I would like to represent each of the regions with the same color (in the image attached) as volumetric surfaces (or interpolated as curves in some meaningful way).

I have tried a variety of approaches, including contour3 plots, etc, but I am looking for suggestions on how I can further improve the visualization of clusters in this 3-dimensional plot of points with the same color.

Additionally, side question, I have a 5-dimensional system where all 5 of the dimensions are mostly uncorrelated. What are some techniques through which I can visualize this system in a 3-dimensional space? One method that I tried is training a MATLAB fitnet neural network that can approximate the fourth dimension based on the other values.

[KSSV]

Attach your data. Have a look on surf, slice.

Answer 1

[Unai San Miguel]

3 dimensions are really hard to plot, it is almost always better to switch to 2D, and better contours than filled contours. If you use contours you can use different colours for other variable: for instance black labelled contour lines for one set and red labelled contours for other set.

If one (or two) of the variables is discrete or if it is meaningful to bin it into discrete values you can use facets (<https://en.wikipedia.org/wiki/Small_multiple>).

As KSSV comments, having some data would help to give better advise.