The paper is a case study of technology-facilitated argumentation. Several graduate students, the first four authors, present and negotiate complementary interpretations of a diagram generated in a computer-simulated stochastic experiment. Individuals use informal visual metaphors, programming, and formal mathematical analysis to ground the diagram, i.e., to achieve a sense of proof, connection, and understanding. The NetLogo modeling-and-simulation environment (Wilensky, 1999) serves to structure the authors’ grounding, appropriating, and presenting of a complex mathematical construct. We demonstrate individuals’ implicitly diverse explanatory mechanisms for a shared experience. We show that this epistemological diversity, sometimes thought to undermine learning experiences, can, given appropriate learning environments and technological fluency, foster deeper understanding of mathematics and science.