Conventional Magnets: Interaction
is Binary

Conventional magnet interaction is binary.  Because one side of each magnet has a positive (or North) polarity and the other side has a negative (or South) polarity, two conventional magnets will either attract or repel each other depending on their polarity orientation.   Because of this binary interaction behavior conventional magnets will naturally stack such that their polls alternate such as shown in Fig. 1.

Fig. 1 Naturally Stacking Conventional Bar Magnets

Two identical structures can be described as being complementary when spatially aligned such that their opposing faces mirror each other as shown in Fig. 2.  In other words, each magnetic source of each of the opposing face is opposite a source having the opposite polarity. 

Fig. 2 Complementary Conventional Magnetic Structures

The five Relative Alignments of the two complementary structures are shown in Fig. 3. 

The possible alignments of the two complementary conventional magnetic field structures correspond to a spatial correlation function depicted in Fig. 4, where aligning magnets either always attract or always repel each other and will seek an attraction orientation.

Fig. 4 Spatial Force Function of Complementary Magnetic Field Structures A and B

Two identical structures can be described as being anti-complementary when spatially aligned such that their equal faces mirror each other as shown in Fig. 2.  In other words, each magnetic source of each of the opposing face is opposite a source having the same polarity. 

Fig. 5 Anti-Complementary Conventional Magnetic Structures

The possible alignments of the two anti-complementary conventional magnetic field structures correspond to a spatial correlation function depicted in Fig. 6, which is opposite the one shown in Fig. 4.

Fig. 6 Spatial Force Function of Anti-complementary Magnetic Field Structures A and B