The article presents the DigiHive system, an artificial chemistry simulation environment, and the results of preliminary simulation experiments leading toward building a self-replicating system resembling a living cell. The two-dimensional environment is populated by particles that can bond together and form complexes of particles. Some complexes can recognize and change the structures of surrounding complexes, where the functions they perform are encoded in their structure in the form of Prolog-like language expressions. After introducing the DigiHive environment, we present the results of simulations of two fundamental parts of a self-replicating system, the work of a universal constructor and a copying machine, and the growth and division of a cell-like wall. At the end of the article, the limitations and arising difficulties of modeling in the DigiHive environment are presented, along with a discussion of possible future experiments and applications of this type of modeling.