Gene Regulatory Networks are networks of interactions in biological organisms responsible for determining the production levels of proteins and peptides. Proteins are workers of a cell factory, and their production defines the goal of a cell and its development. Various attempts have been made to model such networks both to understand these biological systems better and to use inspiration from understanding them to solve computational problems. In this work, a biologically more realistic model for gene regulatory networks is proposed, which incorporates Cellular Automata and Artificial Chemistry to model the interactions between regulatory proteins called the Transcription Factors and the regulatory sites of genes. The result of this work shows complex dynamics close to what can be observed in nature. Here, an analysis of the impact of the initial states of the system on the produced dynamics is performed, showing that such evolvable models can be directed towards producing desired protein dynamics.