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 4n+2, where n is a natural number.

Method
Start by creating a (2n+1)-by-(2n+1) square array consisting of and then exchange the U in the middle with the L above it.
 * n+1 rows of Ls,
 * 1 row of Us, and
 * n-1 rows of Xs,

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:


 * $$\mathrm{L}: \quad \begin{smallmatrix}4&&1\\&\swarrow&\\2&\rightarrow&3\end{smallmatrix} \qquad \mathrm{U}: \quad \begin{smallmatrix}1&&4\\\downarrow&&\uparrow\\2&\rightarrow&3\end{smallmatrix} \qquad \mathrm{X}:\quad \begin{smallmatrix}1&&4\\&\searrow\!\!\!\!\!\!\nearrow&\\3&&2\end{smallmatrix}$$

Example
Let n = 2, so that the array is 5x5 and the final square is 10x10.
 * {| class="wikitable" style="text-align: center"


 * L||L||L||L||L
 * L||L||L||L||L
 * L||L||U||L||L
 * U||U||L||U||U
 * X||X||X||X||X
 * }
 * U||U||L||U||U
 * X||X||X||X||X
 * }
 * }

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.


 * {| class="wikitable" style="text-align: center"


 * width="10%" | 68
 * width="10%" | 65
 * width="10%" | 96
 * width="10%" | 93
 * width="10%" | 4
 * width="10%" | 1
 * width="10%" | 32
 * width="10%" | 29
 * width="10%" | 60
 * width="10%" | 57
 * 66 || 67 || 94 || 95 || 2 ||  3 || 30 || 31 || 58 || 59
 * 92 || 89 || 20 || 17 || 28 || 25 || 56 || 53 || 64 || 61
 * 90 || 91 || 18 || 19 || 26 || 27 || 54 || 55 || 62 || 63
 * 16 || 13 || 24 || 21 || 49 || 52 || 80 || 77 || 88 || 85
 * 14 || 15 || 22 || 23 || 50 || 51 || 78 || 79 || 86 || 87
 * 37 || 40 || 45 || 48 || 76 || 73 || 81 || 84 || 9 || 12
 * 38 || 39 || 46 || 47 || 74 || 75 || 82 || 83 || 10 || 11
 * 41 || 44 || 69 || 72 || 97 ||100 || 5 ||  8 || 33 || 36
 * 43 || 42 || 71 || 70 || 99 || 98 || 7 ||  6 || 35 || 34
 * }
 * 37 || 40 || 45 || 48 || 76 || 73 || 81 || 84 || 9 || 12
 * 38 || 39 || 46 || 47 || 74 || 75 || 82 || 83 || 10 || 11
 * 41 || 44 || 69 || 72 || 97 ||100 || 5 ||  8 || 33 || 36
 * 43 || 42 || 71 || 70 || 99 || 98 || 7 ||  6 || 35 || 34
 * }
 * 41 || 44 || 69 || 72 || 97 ||100 || 5 ||  8 || 33 || 36
 * 43 || 42 || 71 || 70 || 99 || 98 || 7 ||  6 || 35 || 34
 * }
 * }