Cellular automata (CA) have been used to simulate a variety of different chemical, biological and physical phenomena. Their ability to emulate complex dynamics, emerging from simple local interactions of their elementary cells, made them a strong candidate for mimicking these phenomena, especially when accelerated computation through parallelization is required. Belousov–Zhabotinsky (BZ) is a class of chemical reactions that due to their potential as nonlinear chemical oscillators, have inspired scientists to use them as chemical computers. The Oregonator equations, which approximate the dynamics of BZ reactions, were implemented here using CA methods. This new modelling approach (CA-based Oregonator) was tested in terms of accuracy and efficiency against previous models and laboratory-based experimental results, while the benefits of this method were outlined. It was observed that the results from the CA-based Oregonator are in good agreement with both modelled and laboratory experiments. The main advantage of this method can be summarized as the acceleration achieved in current implementations (serial computers), but also towards potential future implementations in massively parallel computational systems (like field-programmable gate array hardware and nano-neuromorphic circuits) that have been proved to be good substrates for accelerating the implemented CA models.