This paper presents a method to solve - in real time the three dimensional workspace generation problem for arbitrary serial manipulators. Our approach is based on Monte Carlo simulation, to process a high number of forward kinematics with randomly chosen joint values. This results in an asymptotic coverage of the reachable workspace. Additionally, collision detection is integrated to consider obstacles within the manipulator's environment. The method is implemented on the graphics processing unit (GPU), such that an extremely high number of workspace points can be processed in parallel. Tests have shown that this approach is capable to generate acceptable workspace coverage within milliseconds. Furthermore, the workspace is held as a three dimensional texture volume on the graphics memory, allowing for instant visualisation of the workspace during the generation process without the need for further time-intensive data exchange.