One of the most well-respected and widely used tools in the study of general intelligence is the Raven's Progressive Matrices test, a nonverbal task wherein subjects must induce the rules that govern the patterns in an arrangement of shapes and figures. This thesis describes the first neurally based, biologically plausible model that can dynamically generate the rules needed to solve Raven's matrices. We demonstrate the success and generality of the rules generated by the model, as well as interesting insights the model provides into the causes of individual differences, at both a low (neural capacity) and high (subject strategy) level. Throughout this discussion we place our research within the broader context of intelligence research, seeking to understand how the investigation and modelling of Raven's Progressive Matrices can contribute to our understanding of general intelligence.