This paper presents a vector painting system for digital artworks. We first propose Temporal Diffusion Curve (TDC), a new form of vector graphics, and a novel random-access solver for modeling the evolution of strokes. With the help of a procedural stroke processing function, the TDC strokes can achieve various shapes and effects for multiple art styles. Based on these, we build a painting system of great potential. Thanks to the random-access solver, our method has real-time performance regardless of the rendering resolution, provides straightforward editing possibilities on strokes both at runtime and afterward, and is effective and straightforward for art production. Compared with the previous Diffusion Curve, our method uses strokes as the basic graphics primitives, which are able to intersect each other and much more consistent with the intuition and painting habits of human. We finally demonstrate that professional artists can create multiple genres of artworks with our painting system.