the work in this thesis makes connections between statistical mechanics and genotype frequencies in population sizes, and how mutation of the bacteria e. coli helps to increase its resistance to the antibiotic ciprofloxacin. the objective of this thesis is to use existing models in statistical mechanics as a basis in order to create a new program to simulate how an antibiotic gradient affects the rate of mutation of a bacterial population, and what influence the shape of the gradient has on the evolutionary rate. in addition, several other factors affecting the evolutionary rate are identified as well. overall, a steeper antibiotic gradient will result in accelerated evolution as long as the initial growth of bacteria is not in the presence of antibiotic. it was observed that by allowing for initial bacterial growth in the absence of antibiotic, followed by migration towards an increasing gradient of antibiotic results in accelerated mutation.