There are features that are pan within pan-magic square. They are patterns whose members add to a constant regardless of the position of the pattern within the pan-magic square, including positions that require wraparound. Among those features are the rows, columns, and diagonals of the square. These three are the minimum requirement for a pan-magic square. The complete and the {2compact2} features are the most commonly mentioned additional pan features. Dame Kathleen Ollerenshaw called pan-magic squares that also have both the complete and {2compact2} features most-perfect.

Within the order-16 pan-magic squares it is also possible to have the corners of all 3x3, 5x5 and/or the 9x9 squares equal S/2, but only two of these in any given square. {Zigzag2} and {zigzag3} lines can also be pan within the magic square. Zigzag lines go back and forth between two or three rows or columns in the magic square. A 2 indicates that the zigzag is between two adjacent lines. A {zigzag3} line involves three adjacent lines. Zigzags will have an abababab pattern for the two lines, a and b, whereas Franklin W diagonals will have an abbaabba pattern.

Other features can be expressed within pan-magic squares that are not pan within the square. These features are only expressed in the magic square that is shown or in a limited number of other transformed squares. The associated property is the most commonly cited example of this type. Inlaid squares are also not pan within the larger pan-magic square but they may themselves be pan-magic and they may have different features than the larger square. Franklin bent diagonals are pan in one direction only. They are pan in the direction the V or W points but not laterally. Both V,W, and WW shaped Franklin bent diagonals are possible in an order-16 square.

Other patterns, both pan and non-pan within the magic square, are present in some order-16 pan-magic squares. Some of these may be accidentally expressed in squares that are generated below but they are not directly supported.


Select the features to be expressed within the magic square
monagonals associated
diagonals Franklin V
half rows Franklin W
complete FranklinWW
{2compact2} 16 order-4
{2compact3} 4 inlaid 4 A
{2compact5} 4 inlaid 4 B
{2compact9} 16 order-8
{zigzag2} 4 inlaid 8's
{zigzag3} 4 center 8's
graphic feature

addendum 6-2-2009

Added half rows feature to generator. This feature requires that each half of every row and every column add to S/2. It is one of the common features in Franklin squares. Note that feature is always true when order 4 squares are presnt in the quadrants, but it can be true on other cases as well.