# Self-complement Magic Squares

## Description

If complementing a magic square results in another aspect of the square itself, the
square is called **self-complement(ary)**. These include the associative squares and squares in which all complement pairs are side-to-side, i.e., left-to-right or top-to-bottom, symmetric.

## Odd Order

All odd order self-complement magic squares are associative.

## Even Order

Doubly-even self-complement magic squares include associative and side-to-side symmetric;
singly-even are only side-to-side symmetric, (there are no singly-even associative magic
squares).

There are 352 order 4 self-complement magic squares, (48 associative, 304 side-to-side
symmetric).

SelfComplementSquares makes side-to-side
symmetric squares using the double border method:

- start with a side-to-side symmetric center
bones of order 4 or 6
- repeatedly add double borders of side-to-side symmetric bones numbers

##### REFERENCES

Heinz, Harvey "Self-similar Magic Squares"
http://recmath.org/Magic%20Squares/Self-similar.htm.

Suzuki, Mutsumi "Magic Squares"
http://web.archive.org/web/20060709213003/http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.html