magic (version 1.3-20)

strachey: Strachey's algorithm for magic squares

Description

Uses Strachey's algorithm to produce magic squares of singly-even order.

Usage

strachey(m, square=magic.2np1(m))

Arguments

m

magic square produced of order n=2m+1

square

magic square of order 2m+1 needed for Strachey's method. Default value gives the standard construction, but the method will work with any odd order magic square

Details

Strachey's method essentially places four identical magic squares $2m+1$ together to form one of $n=4m+2$. Then $0,n^2/4/n^2/2,3n^2/4$ is added to each square; and finally, certain squares are swapped from the top subsquare to the bottom subsquare.

See the final example for an illustration of how this works, using a zero matrix as the submatrix. Observe how some 75s are swapped with some 0s, and some 50s with some 25s.

See Also

magic.4np2,lozenge

Examples

strachey(3)
 strachey(2,square=magic(5))

 strachey(2,square=magic(5)) %eq%  strachey(2,square=t(magic(5)))
 #should be FALSE

 #Show which numbers have been swapped:
 strachey(2,square=matrix(0,5,5))

 #It's still magic, but not normal:
  is.magic(strachey(2,square=matrix(0,5,5)))