Although introductory courses in special relativity give an introduction to the causal structure of Minkowski space, it is common for causal structure in general space- times to be regarded as an advanced topic, and omitted from introductory courses in general relativity, although the related topic of gravitational lensing is often included. Here a numerical approach to visualizing the light cones in exterior Schwarzschild space taking advantage of the symmetries of Schwarzschild space and the conformal invariance of null geodesics is formulated, and used to make some of these ideas more accessible. By means of the Matlab software developed, a user is able to produce figures showing how light cones develop in Schwarzschild space, starting from an arbitrary point and developing for any length of time. The user can then interact with the figure, changing their point of view, or zooming in or out, to investigate them. This approach is then generalised, using the symbolic manipulation facility of Matlab, to allow the user to specify a metric as well as an initial point and time of development. Finally, the software is demonstrated with a selection of metrics.