The chapter introduces the concept of Combinatory Automaton, a tool for simulating, mainly in probabilistic terms, the different classes of combinatory systems. Combinatory Automata models offer a simulation of the dynamics of combinatory systems in terms of the dynamics, expressed in probability terms, of the state of the system and the state of the individual elements. A Combinatory Automaton is composed of a matrix, each of whose cells contains a variable representing the state of an agent. The value of each cell at time th depends on a synthetic global variable whose values derive from some “combination” operation carried out on the values of the cells in successive iterations; the synthetic global variable represents the synthetic state of the automaton. The micro-macro feedback operating in successive moments for a certain period connects the analytical values of the cells and the synthetic state of the automaton. This chapter seeks to demonstrate, through simple examples, that combinatory systems represent a wide range of behaviors of collectivities and that Combinatory Automata are a powerful tool for simulating the most relevant combinatory systems.