How do I visualize an $n$-dimensional function?

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How do I visualize the concept of a function that has more than three dimensions in the context of noise functions?

I understand that a one-dimensional function as a function that can be plotted in a Cartesian plane, like this.

And I understand that a two-dimensional function could be represented in a grid, and a third dimension could represent e.g. a time dimension or a 3-D representation.

But I have trouble understanding the concept of functions with say, six or more, dimensions. I rationally understand the concept that such a function would return values represented by sets of n coordinates, but how do I picture something like that?