Visualizations enable scientists to inspect, interpret, and analyze large multi-dimensional data sets. Effective visualizations are designed to both orient and engage viewers by directing attention in response to a visual stimulus, and then encouraging a viewer's vision to linger at a given image location. Research into human visual perception provides information about how to orient viewers, using salient visual features, such as color, orientation, and flicker. Less is known about how to build engaging visualizations. Increasing the aesthetic merit of visualizations is a promising approach to increasing engagement. Intuition suggests that visualizations with a more aesthetic presentation style will be judged as more artistic, but this is an open problem. In this thesis, we explored an important question pertaining to creating aesthetic visualizations: Is it possible to affect the perceived artistic merit of a scientific visualization? To investigate this question, we developed three new painterly visualization techniques, designed to vary different visual qualities important to aesthetics: interpretational complexity (IC), indication and detail (ID), and visual complexity (VC). We conducted four experiments to investigate how these qualities affect the aesthetics. Observers were asked to rank IC, ID, and VC images, together with Master abstract and Impressionist paintings on five questions: artistic merit, pleasure, arousal, meaningfulness, and complexity. Although realistic Impressionist paintings consistently ranked as most artistic, computer visualizations were considered as artistic as and more pleasing than Master abstractionist artwork in certain situations. There was also a significant preference for aesthetic visualizations that used more sophisticated presentation styles. This provides strong evidence that our aesthetic techniques can increase the perceived artistic merit of a visualization, possibly leading to a significant improvement in the visualizations's ability to engage its viewers. We applied our experimental techniques to real meteorological and supernova data sets, to explore their capabilities in a real-world setting. Anecdotal feedback from a domain expert in astrophysics was strongly positive, further supporting the theory that enhancing the artistic merit of visualizations is a worthwhile contribution to the scientific community.