Max-plus algebraic agent description and its application to various social systems

Max-plus algebra which is composed of max and standard addition operations, is essentially suitable for discrete information processing and is has different mathematical structure compared with the ordinal algebra. Natural phenomenon and various social systems can be described by cellular automata and percolation which are based on max-plus algebra. Furthermore, complex network is also defined by percolation in the setting of generalized lattice structure. This paper presents description of cellular automata and percolation based on max-plus algebra, furthermore, shows various social systems based on cellular automata and percolation: the traffic flow simulation, forest fire, and epidemic simulation.