# Multidimensional array

Multidimensional arrays are arrays with two or more dimensions, i.e. tables with values for "rows", "columns" and possibly for additional "axes" or "coordinates".

3-dimensional arrays can be used to give positions of things in a 3-dimensional space (length, width, height), 4-dimensional arrays for positions in space-time (length, width, height, time), etc.

Because papers and computer screens are 2-dimensional, arrays with higher number of dimensions are hard to visualize. The following 3-dimensional array `A` indexed by three indexes, `Index_a`, `Index_b` and `Index_c`, serves as an example of a simple multi-dimensional array:

`Variable A :=`
`Index_c = 'displayed value'`
Index_b ▶
Index_a ▼ a b c
x value value value
y value value value
z value value value

As another example of a 3D array, consider the array `Colors` indexed by `Number`, `Letter`, and `Hue`:

`Variable Colors :=`
Number ▶
Letter ▼ 1 2 3
A 45 19 92
B 13 21 81
C 12 43 47

`Hue = 'Red'`

Number ▶
Letter ▼ 1 2 3
A 34 25 45
B 11 62 19
C 84 45 53

`Hue = 'Green'`

Number ▶
Letter ▼ 1 2 3
A 21 65 95
B 48 33 12
C 57 56 23

`Hue = 'Blue'`

Compare these multi-dimensional arrays to the following arrays with fewer dimensions:

An index or list and its values:

`Index N :=`
 1 2 3 4 5

A one-dimensional array:

`Variable Squares :=`
Squares ▶
1 2 3 4 5
1 4 9 16 25

A two-dimensional array:

Index_b ▶
Index_a ▼ a b c
x value value value
y value value value
z value value value