Colloidal gold nanospheres have been used in a variety of applications since the Middle Ages, when artisans blended tissue paper thin gold sheets into molten glass, creating stained glass panels with rich ruby red hues. Despite both substantial interest and well-established procedures for producing nanoparticles of various shapes, little is known about the growth mechanisms that govern the formation of shapes such as rods, cubes, tetrahedrons, and dog-bones. Understanding these mechanisms is an important step in developing applications using nanoparticles. With more finely defined controls, metallic nanoparticles could be fabricated or grown in desired shapes with far less trial and error, offering greater potential for complex and functional nanostructures. In this work, a cellular automata model is used to model the growth of high aspect ratio gold nanorods. One mechanism that has been suggested for nanorod growth is competitive binding between the colloidal gold in solution and a surfactant, which functions as a structure-directing agent. The model incorporates experimental conditions in the framework of this competitive binding. Results suggest that cellular automata modeling can be a computationally efficient means of modeling the competitive and non-deterministic interactions involved in the growth of gold nanorods.