To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomycete Mucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffuses into the surrounding medium and is detected by the growing hyphae. We also present a simple Markovian growth model without such a feedback, but yielding to analytical computations.