Conway's LUX method for magic squares
Conway's LUX method for magic squares is an algorithm by John Horton Conway for creating magic squares of order 4"n"+2, where "n" is a natural number. Method. Start by creating a (2"n"+1)-by-(2"n"+1) square array consisting of and then exchange the U in the middle with the L above it. Each letter represents a 2x2 block of numbers in the finished square. Now replace each letter by four consecutive numbers, starting with 1, 2, 3, 4 in the centre square of the top row, and moving from block to block in the manner  of the Siamese method: move up and right, wrapping around the edges, and move down whenever you are obstructed. Fill each 2x2 block according to the order prescribed by the letter: Example. Let "n" = 2, so that the array is 5x5 and the final square is 10x10. Start with the L in the middle of the top row, move to the 4th X in the bottom row, then to the U at the end of the 4th row, then the L at the beginning of the 3rd row, etc.