The use of random algorithms in many areas of computer science has enabled the solution of otherwise intractable problems. In this paper we propose that random sampling can make the visualisation of large datasets both more computationally efficient and more perceptually effective. We review the explicit uses of randomness and the related deterministic techniques in the visualisation literature. We then discuss how sampling can augment existing systems. Furthermore, we demonstrate a novel 2D zooming interface – the Astral Telescope Visualiser, a visualisation suggested and enabled by sampling. We conclude by considering some general usability and technical issues raised by sampling-based visualisation.