Suggestions for a method of analyzing binary images using Langlet's parity logic

This paper describes an extension to the system of parity logic operations developed by Gerard Langlet and subsequently elaborated by Michael Zaus. Two operations, A and B , are introduced which can be used both to analyze and to synthesize arbitrary patterns of l's and O's in square Boolean matrices. The A and B operations are, like most of the operations in Langlet's system, completely reversible (i.e., the input to A or B can be exactly reconstructed its output). The B operation is shown to be connected with Langlet's Helical and Cognitive transforms. Manipulations of binary images are used to illustrate the properties of A and B , but no claim made that they have real-world applications at this time. The A and B algorithms, their supporting operations, and the programming examples are in Q'Nial; however, they can be easily translated APL, J, or other may programming language.