This paper presents an approach to “rich” digital calligraphy pens. These pens draw strokes consisting of an elaborate ornamental structure in real time. The structure’s density and complexity depend on the stroke width which itself is controlled by the pen pressure. In particular, we describe a process that, driven by pen data and applied during the drawing process, dynamically combines variable basic building blocks to create aesthetically pleasing ornaments within the stroke. In addition to the algorithmic challenges posed by the real-time scenario, we address several mathematical problems as diverse as discrete conformal mappings, the geometric properties of logarithmic spirals, and the generation of fractal branching structures.