Constraint satisfaction problems, found in many areas and domains of computer science, return solutions that satisfy given constraints. When given a single solution out of the solution space from a general-purpose solver users may want to further explore other alternatives to find ones that better meet their aims or to verify the believability of the existing result. However, users attempting to examine the solution space are often confronted with a state explosion problem, leaving them with the unrealistic task of manually sifting through each state. We aimed to assist users in exploring state spaces more efficiently. Using the concrete semantics of requirements modeling in the Evolving Intentions framework, we contribute two visualization techniques: (1) valuation-based coloring to assist users in interpreting the results of the path-based analysis and selecting states from the solution space more efficiently, and (2) valuation-based filtering to reduce the number of states in the solution space. Using a motivating example, we demonstrate the need for state space visualization and we provide an initial validation of our results. These visualization techniques can be used beyond the Evolving Intentions framework, to be adapted to other areas in software engineering.