This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain. We propose a modified definition of autopoiesis: An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network. We also propose a definition of cognition: A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint. It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: A system that is both autopoietic and cognitive is a living system.