There is increasing evidence that users' characteristics such as cognitive abilities and personality have an impact on the effectiveness of information visualization techniques. This paper investigates the relationship between such characteristics and fine-grained user attention patterns. In particular, we present results from an eye tracking user study involving bar graphs and radar graphs, showing that a user's cognitive abilities such as perceptual speed and verbal working memory have a significant impact on gaze behavior, both in general and in relation to task difficulty and visualization type. These results are discussed in view of our long-term goal of designing information visualisation systems that can dynamically adapt to individual user characteristics.