In the difficult ab initio prediction in protein folding only the information of the primary structure of amino acids is used to determine the final folded conformation. The complexity of the interactions and the nature of the amino acid elements are reduced with the use of lattice models like HP, which categorizes the amino acids regarding their hydrophobicity. On the contrary to the intense research performed on the direct prediction of the final folded conformation, our aim here is to model the dynamic and emergent folding process through time, using the scheme of cellular automata but implemented with artificial neural networks optimized with Differential Evolution. Moreover, as the iterative folding also provides the final folded conformation, we can compare the results with those from direct prediction methods of the final protein conformation.