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Visualising computational simulation models of solid state physical systems is a hard problem for dense lattice models. Fly-throughs and cutaways can aid viewer understanding of a simulated system. Interactive time model parameter updates and overlaying of measurements and graticules, cluster colour labelling and other visual highlighting cues can also enhance user intuition of the model’s meaning. We present some graphical and simulation optimisation techniques and various graphical rendering and explanatory techniques for computational simulation models such as the Ising model in 2 and 3 dimensions. In addition to aiding understanding of conventional algorithms such as Metropolis Monte Carlo, we try to visualise cluster updates to the system using algorithms like that of Wolff. We also explore ways to visualise path-length shortening and other changes to the Ising system when small-world link rewiring is applied to the system. We use a combination of OpenGL visualisation software and General Purpose Computing on Graphics Processing Units (GPGPU) with the Compute Unified Device Architecture (CUDA) and consider ways to accelerate both the simulation itself as well as the graphical rendering to make an interactive system of model system sizes that are large enough to be challenging and visually interesting

Visualising spins and clusters in regular and small-world Ising models with GPUs