Visualising a scalar valued function of the form $f(x,y,z) = w$

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I am trying to simulate the saturation for a colour. I know there might be a good proper way but I'm only doing it to better understand some concepts.

The saturation is one value while a colour can be represented as a three dimensional vector with minimum value $(0,0,0)$ and maximum value $(1,1,1)$.

I did some experimentation and figured that the three norm for such a vector would give me a value between $0$ and $1$, the way I wanted it.

What this means is:

$f(x,y,z) = \sqrt[3]{x^3 + y^3 + z^3}$

I wish to visualise this function.

I am guessing that a transformation is the way to go.

Also, the 2 norm has the name "Euclidean norm" (for good reason), is there a name for the 3 norm as well?