This article discusses how visual arts and computer technology could complement and assist each other in new and emerging interdisciplinary areas known as computational aesthetics and aesthetic computing. The authors present examples of computational aesthetics that demonstrate that modern computer technology can generate aesthetic forms of visual art. Several levels of complexity in computerized abstract paintings are discussed and explored. The authors recently experimented with encoding computational rules to automatically generate a particular style of abstract painting in an attempt to explore one of the levels. The preliminary results of this research are presented. A more systematic and grammar-based approach is discussed as a potential future direction of work.