One of the pressing issues addressed by complex systems research is identifying the conditions under which emergent phenomena arise. For instance, an ant colony is essentially an emergent structure, consisting of many individuals who have no global knowledge of their system. Questions such as this have been widely studied in many forms using logical universes called cellular automata. These studies investigate how local interactions, or connections, produce a global coordinated computation. This seminar will provide a brief review of some notable work on emergent computation and discuss further issues of the relationship between connectivity and emergent computational behavior.