Beta cells in pancreatic islets release the hormone insulin in response to elevated glucose. Gap junctional coupling between these cells tends to synchronize bursting, which drives release. However, heterogeneity within the islet leads to counterintuitive emergent bursting behavior. We have developed the computational islet, a three-dimensional network, to capture the impact of variation in cells and their connectivity, glucose exposure, and coupling strength on bursting. Numerical advances have sped up computation of 1000-cell islet by up to two orders of magnitude. We exhibit these for a 7-variable and a 3-variable model. We show that the peak of a non-monotonic average burst period vs. coupling strength curve depends monotonically on a connectivity measure of slow and fast cells in each model. In certain situations we can get emergent bursting that is slower than the slowest cells bursting alone, which has been observed in coupled cell models, and is connectivity dependent. Finally, we show that the computational islet supports waves of calcium in a model of high glucose flow on the edge of an islet reminiscent of experiments.