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 square array consisting of

n+1 rows of Ls,
1 row of Us, and
n-1 rows of Xs,

each row having length 2n+1.

Now exchange the U in the middle with the L above it.

Using the Siamese method generate a magic square of order 2n+1 overlaying the array of letters, beginning from the center square of the top row. Now fill each square 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}}

An example square, of order 10, follows:

68	65	96	93	4	1	32	29	60	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

Method

See also