Abstract: The problem of global illumination in computer graphics is described by a second kind of Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-random walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks is also applicable to transport problems in settings other than computer graphics.