Three-dimensional simulation models are hard to visualise for dense lattice systems, even with cutaways and flythrough techniques. We use multiple Graphics Processing Units (GPUs), CUDA and OpenGL to increase our understanding of computational simulation models such as the 2-D and 3-D Ising systems with small-world link rewiring by accelerating both the simulation and visualisation into interactive time. We show how interactive model parameter updates, visual overlaying of measurements and graticules, cluster labelling and other visual highlighting cues enhance user intuition of the model’s meaning and exploit the enhanced simulation speed to handle model systems large enough to explore multi-scale phenomena.