What methods are used to visualize a 4-dimensional Array?

Question

An Array ( a row of elements ):

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A 2-D Array ( a table ):

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A 3-D Array:

//Imagine the above table as a cube ( a table with depth )

How does one visualize a 4-D array?

The closest I can come is multiple cubes, so for int[,,,] [5,10,2,7] would be cube 5, row 10, column 2, layer(depth) 7.

I'm not sure if this is the best way to visualize a 4-D array, though... and I'm not sure it's the best way to teach it... however it does have the advantage of being extensible ( a row cubes, a table of cubes, a cube of cubes ( 6-d array )

Cubes through time is another way that I can think of it.

Am I on the right track here?

Answer 1

If you're trying to display output of a program for end users, then you are on the right track.

If you're trying to teach it, I'd briefly use that method, and then I'd go into depth explaining how the computer keeps them all in contiguous memory -- http://www.plantation-productions.com/Webster/www.artofasm.com/Windows/HTML/Arraysa2.html. I think this is the best way to understand it.

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The original link is no longer working, but I found it up on the Internet Archive here -- http://web.archive.org/web/20120410120743/http://webster.cs.ucr.edu/AoA/Windows/HTML/Arraysa2.html

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Updated first paragraph to show updated link, thanks to @OskensoKashi.

Answer 2

That's how I would teach it: a row of cubes. The position (or cube number) on this row is the 4th dimension.

And if you want 5-dimensions, now picture columns and rows - of cubes!

For 6 dimensions, picture the rows and columns of cubes (as for 5 dimensions), and now add "layers" of these rows and columns.

...For 7 dimensions, imagine all of the above - contained in cubes in a single row! ;)

Yup, it's cubes all the way down.