Both natural and manufactured surfaces have been found to be self-affine over many length scales. Yet, it is still not understood what mechanisms lead to the final self-affine morphology, which is characterized by a persistent Hurst exponent (greater than 0.5, see next section 2.1 for the definitions). The scope of this project is then to develop new discrete growth models that can help gather insights in the formation of self-affine surfaces in frictional processes.