Franklin Squares
Part 2
My Construction Method

16x16 Square B
0	15	0	15	0	15	0	15	0	15	0	15	0	15	0	15
1	14	1	14	1	14	1	14	1	14	1	14	1	14	1	14
15	0	15	0	15	0	15	0	15	0	15	0	15	0	15	0
14	1	14	1	14	1	14	1	14	1	14	1	14	1	14	1
2	13	2	13	2	13	2	13	2	13	2	13	2	13	2	13
3	12	3	12	3	12	3	12	3	12	3	12	3	12	3	12
13	2	13	2	13	2	13	2	13	2	13	2	13	2	13	2
12	3	12	3	12	3	12	3	12	3	12	3	12	3	12	3
4	11	4	11	4	11	4	11	4	11	4	11	4	11	4	11
5	10	5	10	5	10	5	10	5	10	5	10	5	10	5	10
11	4	11	4	11	4	11	4	11	4	11	4	11	4	11	4
10	5	10	5	10	5	10	5	10	5	10	5	10	5	10	5
6	9	6	9	6	9	6	9	6	9	6	9	6	9	6	9
7	8	7	8	7	8	7	8	7	8	7	8	7	8	7	8
9	6	9	6	9	6	9	6	9	6	9	6	9	6	9	6
8	7	8	7	8	7	8	7	8	7	8	7	8	7	8	7
16x16 Square A
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
0	1	15	14	2	3	13	12	4	5	11	10	6	7	9	8
15	14	0	1	13	12	2	3	11	10	4	5	9	8	6	7
magic square
1	242	16	255	3	244	14	253	5	246	12	251	7	248	10	249
32	239	17	226	30	237	19	228	28	235	21	230	26	233	23	232
241	2	256	15	243	4	254	13	245	6	252	11	247	8	250	9
240	31	225	18	238	29	227	20	236	27	229	22	234	25	231	24
33	210	48	223	35	212	46	221	37	214	44	219	39	216	42	217
64	207	49	194	62	205	51	196	60	203	53	198	58	201	55	200
209	34	224	47	211	36	222	45	213	38	220	43	215	40	218	41
208	63	193	50	206	61	195	52	204	59	197	54	202	57	199	56
65	178	80	191	67	180	78	189	69	182	76	187	71	184	74	185
96	175	81	162	94	173	83	164	92	171	85	166	90	169	87	168
177	66	192	79	179	68	190	77	181	70	188	75	183	72	186	73
176	95	161	82	174	93	163	84	172	91	165	86	170	89	167	88
97	146	112	159	99	148	110	157	101	150	108	155	103	152	106	153
128	143	113	130	126	141	115	132	124	139	117	134	122	137	119	136
145	98	160	111	147	100	158	109	149	102	156	107	151	104	154	105
144	127	129	114	142	125	131	116	140	123	133	118	138	121	135	120

The simplest and most obvious is to produce a square with imbedded squares. Using column one square B as the sequence in row one square A will do that. All the features in square B will be in square A 90 degrees out of phase. All of the main Franklin features will remain as well as most if not all of the lesser features. In fact some features that were horizontal only in his original 8x8 and 16x16 will become horizontal and vertical.

Review the square with imbedded squares on My Squares Part 2. The wraparound of the bent diagonals can be explained by examining the component squares. In square B all the numbers in the wraparound are the same when started in any odd column. In square A there are two complimentary pairs, one pair in rows four and five, the other in rows three and six. Those pairs will always be complimentary pairs no matter where they are placed. Any pair of cells in a column will be a complimentary pair if one element is in an odd row and the other in an even row. The wraparound will always produce the proper total if wrapped around into any odd column.

This construction is general for all multiples of eight.

Return to My Contruction Method Part 1

Continue to My Contruction Method Part 3