Graphic designers have been producing infographics and charts well before the recent proliferation of computer generated visualizations. As visualization becomes an increasingly popular medium for storytelling and communication, there is a renewed and growing interest to understand visualization creation from the perspective of graphic design. To solve this problem, we propose a novel visual language that describes the composition and generation of diverse visualizations based on the "lazy data binding" approach. This language builds on familiar graphic design concepts such as vector paths, anchor points and segments, and introduces novel primitives for data-driven authoring. Data Illustrator offers direct manipulation techniques for easy and flexible visualization authoring. We demonstrate the expressive power of our approach through a range of well-known, real-world examples.