Universality of Growth Rules in Fractal Growth

We consider the problem of the universality of growth rules in fractal-growth models and introduce a theoretical scheme that allows us to address this question. In particular we show that growth defined per site and rules that include diagonal processes renormalize asymptotically into effective growth rules of simple bond type. Therefore, we identify the general nature of the asymptotic, scale-invariant growth dynamics for coarse-grained variables.