magic - Magic square - MATLAB (original) (raw)

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Syntax

Description

M = magic([n](#d126e1032165)) returns ann-by-n matrix constructed from the integers 1 throughn2 with equal row and column sums. The order n must be a scalar greater than or equal to3 in order to create a valid magic square.

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Examples

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Compute the third-order magic square M.

M = 3×3

 8     1     6
 3     5     7
 4     9     2

The sum of the elements in each column and the sum of the elements in each row are the same.

Visually examine the patterns in magic square matrices with orders between 9 and 24 using imagesc. The patterns show that magic uses three different algorithms, depending on whether the value of mod(n,4) is 0, 2, or odd.

for n = 1:16 subplot(4,4,n) ord = n+8; m = magic(ord); imagesc(m) title(num2str(ord)) axis equal axis off end

Input Arguments

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Matrix order, specified as a scalar integer greater than or equal to 3. Ifn is complex, not an integer, or not scalar, thenmagic converts it into a usable integer withfloor(real(double(n(1)))).

If you supply n less than 3, thenmagic returns either a nonmagic square, or the degenerate magic squares 1 and[].

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char

Extended Capabilities

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Usage notes and limitations:

• The input argument n must be a constant at code generation time.

Version History

Introduced before R2006a