This paper will attempt a syntheses of the two strands of geographic information science: visualization on the one hand and geocomputation on the other. First, each will be defined and then how they are beginning to inform one another will be considered. In essence, it is argued that visualization is one of the main tools in understanding how complex spatial systems work. Good models of spatial systems which are geocomputable in various ways, must emphasize structure and process in space and time and thus one of the main tasks of visualization is to enhance our understanding of such processes. Visualization can be used in many ways although the focus here is upon using such tools to visualize how processes work as well as how spatial structures evolve. Such techniques will be classified into: those which enable visualization of the process, those that enable visualization of structures, those that enable visualization of error, and those that enable visualization of the future, of geocomputation which is focused on prediction and prescription. Several examples taken from projects currently being developed at the Centre for Advanced Spatial Analysis (CASA) at UCL, ranging from visualization of ancient Egypt, to large scale 3-D visualization of cities, to processes of urban change based on cellular automata and agent-based models, to the role of visualization in constructing a new urban geography will be shown.