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

See Also

• Tutorial: Arrays
• Arrays and Indexes
• Array Function Example Variables
• Array-reducing functions
• Relational tables and multiD arrays
• Array Manipulation Examples and Challenge Problems
• Implicit Dimensions