Nonequilibrium roughening transition in a simple model of fungal growth in 1+1 dimensions

We introduce a simple model of yeast-like growth of fungi colonies, which exhibits a continuous roughening transition far from equilibrium from a smooth ($\alpha = 0$) to rough phase ($\alpha = 1/2$) in 1+1 dimensions. At the transition some scaling exponents are calculated by mapping the problem onto a directed percolation process. The model reproduces the roughening transition observed in some experiments of fungal growth