My work in the NKS Summer School 2003 was concerned with so-called symbolic systems. Wolfram (2002) presents symbolic systems as one class of simple programs, besides cellular automata, Turing machines, register machines, and others. The evolution of a symbolic system consists in the application of a set of one or more rules of the form lhs -> rhs to an initial expression. Following the directions set by Wolfram (2002), the simplest forms of symbolic systems were investigated, in search for the threshold of complex behavior. The parameters investigated were number of rules, number of operators, and the size of lhs and rhs, as well as the size of the initial conditions. It was found that the threshold of complexity is reached with rather small sizes of rules and initial conditions. Other issues dealt with were how to visualize symbolic systems and how the evaluation scheme used to apply the rules affects the evolution of the system.