Algebraic property of flow diagram in a time-reverse cellular automaton

The autonomously emerging boundary model (AEB) is a basic and probably intrinsic model for living things or an irreversible system. It is formulated using an elementary cellular automaton and features the operation of the time-reverse rule. The time-reverse rule could contradict the ordinary temporal rule, and we can express the discrepancy between the macroscopic rule and the microscopic rule. In this paper we show the short procedure of AEB and the new recipe for the flow diagram, which is a reference for the time-reverse rule (primitive FD). It is also shown that we can obtain the class of box in the flow diagram and that the flow diagram is closed. In particular we show the feature of the primitive FD of the symmetric rule.