strachey {magic}

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 of order 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.

Author(s)

Robin K. S. Hankin

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)))