An approach to pattern operations on a two-dimensional iterative network - A system of operations of local functions

This paper explores the basic properties of a two-dimensional iterative network with binary input and output such that (1) the set of all local functions which represent a mapping from input to output forms a Boolean algebra, (2) an arbitrary local function can be represented by a function which corresponds to shifting of the input to each cell, and (3) a composite function of arbitrary local functions can be represented by a Boolean algebra of functions corresponding to shifting. Based on this exploration, it is shown that a system of operations consisting of Boolean operations of local functions and composite operations of local functions can clearly describe the procedure necessary for pattern operations on a two-dimensional iterative network.