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 {^{2}compact_{2}} features are the most commonly mentioned additional pan features. Dame Kathleen Ollerenshaw called pan-magic squares that also have both the complete and {^{2}compact_{2}} 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. {Zigzag_{2}} and {zigzag_{3}} 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 {zigzag_{3}} 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.
monagonals | associated |
diagonals | Franklin V |
half rows | Franklin W |
complete | FranklinWW |
{^{2}compact_{2}} | 16 order-4 |
{^{2}compact_{3}} | 4 inlaid 4 A |
{^{2}compact_{5}} | 4 inlaid 4 B |
{^{2}compact_{9}} | 16 order-8 |
{zigzag_{2}} | 4 inlaid 8's |
{zigzag_{3}} | 4 center 8's |
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.