The central theme of this project revolves around some specific epistemological aspects of the science of morphology. It is argued that the possibility for defining such a science relies heavily upon models, and more specifically upon mathematical modeling. The concept of morphospace is central to this debate, since it unifies mathematical modeling with the expectations on morphological transformations given a set of rules. Thus, a morphospace allows the analysis of a given morphology by contrasting it with a set of related but impossible forms. As a practical exercise, it is proposed to build a morphospace based on cellular automata models of tetrapod skeletons. These models should allow to run controlled simulations of ontogenetic and phylogenetic change. The different outputs from these simulations will define a morphospace that will be used as a framework in which other biological questions can be assessed (e.g., function, adaptation, evolutionary change, developmental change, etc.). Special attention will be given to the tetrapod limb system and the pelvic girdle, but other structures will be modeled as well.