Budding yeasts, such as Saccharomyces cerevisiae (baker's yeast), that are grown on a solid substrate are able to alter their growth pattern to suit the surrounding nutrient level. When nutrient is readily available, buds separate from the mother cell to produce colonies that appear close to circular when viewed from above. When nutrient is limited, the cells reproduce via the pseudohyphal growth pattern, which is characterised by distal unipolar budding (budding opposite to the birth scar), the elongation of cells and a persistent connection between mother and daughter cell. This change results in the growth of filaments directed away from the colony, producing an irregular shape. The precise shape of the colony is dependent on several factors, such as the nutrient level and strain, while gene-deletion mutants may also display different morphologies. As these have an influence at the cell level, there is a need to understand how the behaviour of individual cells influences the overall colony morphology. To address this, yeast colony growth is studied using an agent-based mathematical model. The model allows for the control of nutrient diffusion and budding mechanism, including the change in cell behaviour during the pseudohyphal phase. Simulations using this model are found to compare favourably with experimental observations and are used to illustrate the relationship between the behaviour of individual cells and the overall colony shape.