The carved and painted decorations in traditional Batak houses and buildings, gorga, are the source of their exoticism. There are no identical patterns of the ornaments within Batak houses and the drawings are closely related to the way ancient Batak capture the dynamicity of the growing “tree of life”, one of central things within their cosmology and mythology. The survey of ornaments of Batak houses and buildings in Northern Sumatera Indonesia has made us possible to observe the complex pattern. The fractal dimensions of the geometrical shapes in gorga are calculated and they are conjectured into 1.5-1.6, between the dimensional of a line and a plane. The way gorga is drawn is captured by using some modification to the turtle geometry of L-System model, a popular model to model the dynamics of growing plants. The result is a proposal to see Bataknese gorga as one of traditional heritage that may enrich the studies to the generative art.