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In this paper, we show that many complex patterns, which characterize the decorative style of many artisanal objects, can be generated by the recursive application of only four operators. Each operator is derived from tracing the isolines or the integral curves of geodesics fields generated from selected seeds on the surface. Based on this formulation, we present an interactive application that lets designers model complex recursive patterns directly on the object surface, without relying on parametrization. We support interaction on commodity hardware on meshes of a few million triangles, by combining light data structures together with an efficient approximate graph-based geodesic solver. We validate our approach by matching decoration styles from real-world photos, by analyzing the speed and accuracy of our geodesic solver, and by validating the interface with a user study.