### Most perfect transformation

You can transform a 8x8 square with consecutive numbers into a Franklin panmagic 8x8 square in the following 5 steps.  Swap each time 'yellow' and 'red':

 # * * # 1 9 17 25 33 41 49 57 1 9 57 49 33 41 25 17 1 9 57 49 33 41 25 17 2 10 18 26 34 42 50 58 2 10 58 50 34 42 26 18 2 10 58 50 34 42 26 18 3 11 19 27 35 43 51 59 # 3 11 59 51 35 43 27 19 8 16 64 56 40 48 32 24 4 12 20 28 36 44 52 60 * 4 12 60 52 36 44 28 20 7 15 63 55 39 47 31 23 5 13 21 29 37 45 53 61 5 13 61 53 37 45 29 21 5 13 61 53 37 45 29 21 6 14 22 30 38 46 54 62 6 14 62 54 38 46 30 22 6 14 62 54 38 46 30 22 7 15 23 31 39 47 55 63 * 7 15 63 55 39 47 31 23 4 12 60 52 36 44 28 20 8 16 24 32 40 48 56 64 # 8 16 64 56 40 48 32 24 3 11 59 51 35 43 27 19 1 16 57 56 33 48 25 24 1 16 57 56 33 48 25 24 1 16 57 56 33 48 25 24 2 10 58 50 34 42 26 18 58 50 2 10 26 18 34 42 63 50 7 10 31 18 39 42 8 9 64 49 40 41 32 17 8 9 64 49 40 41 32 17 8 9 64 49 40 41 32 17 7 15 63 55 39 47 31 23 63 55 7 15 31 23 39 47 58 55 2 15 26 23 34 47 5 12 61 52 37 44 29 20 5 12 61 52 37 44 29 20 5 12 61 52 37 44 29 20 6 14 62 54 38 46 30 22 62 54 6 14 30 22 38 46 59 54 3 14 27 22 35 46 4 13 60 53 36 45 28 21 4 13 60 53 36 45 28 21 4 13 60 53 36 45 28 21 3 11 59 51 35 43 27 19 59 51 3 11 27 19 35 43 62 51 6 11 30 19 38 43

Use this method to construct magic squares of order is multiple of 4 from 4x4 to infinity. See 4x48x812x1216x1620x2024x2428x2832x32

8x8, Most perfect transformation.xls