There's a magic square described in the book Necroscope by
Brian Lumley with some interesting properties and an interesting
method of construction. It's so simple but so powerful the memory
of this trick has stuck with me years after reading the book.
This square also has some historical
meaning.

Take a magic square, 4x4, and fill it in just by counting from 1-16:

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Now the idea behind this method is to use a simple

mechanism to achieve
an

equal distribution of the numbers. Take the diagonal, {1,6,11,16},
and flip it so it becomes {16,11,6,1}:

**16** 2 3 4
5 **11** 7 8
9 10 **6** 12
13 14 15 **1**

Now do the same to the {4,7,10,13} diagonal:

16 2 3 **13**
5 11 **10** 8
9 **7** 6 12
**4** 14 15 1

Each row, column and diagonal adds up to 34, but that's just like any other magic square. The cool thing about this one is that the following patterns also add up to

34:

**16** 2 3 **13** 16 2 3 13
5 11 10 8 5 **11** **10** 8
9 7 6 12 9 **7** **6** 12
**4** 14 15 **1** 4 14 15 1
16 **2** **3** 13 16 2 3 13
5 11 10 8 **5** 11 10 **8**
9 7 6 12 **9** 7 6 **12**
4 **14** **15** 1 4 14 15 1

Working with permutations of these patterns will also give you a sum of 34:

**16** **2** 3 13 16 2 **3** **13**
5 11 10 8 5 11 10 8
**9** **7** 6 12 9 7 6 12
4 14 15 1 **4** **14** 15 1