We discuss the inter-relationship between various concepts of complexity by introducing a complexity "triangle" featuring objective complexity, subjective complexity and social complexity.  Their connections are explored using visual and musical compositions of art. As examples, we quantify the complexity embedded within the paintings of the Jackson Pollock and the musical works of Johann Sebastian Bach. We discuss the challenges inherent in comparisons of the spatial patterns created by Pollock and the sonic patterns created by Bach, including the differing roles that time plays in these investigations. Our results draw attention to some common intriguing characteristics suggesting "universality" and conjecturing that the fractal nature of art might have an intrinsic value of more general significance.