A new computer graphics algorithm which simulates the propagation of light and its interaction with matter on a massively parallel machine is presented. This algorithm, called the Tagged Shooting Method, is designed for a virtual computer containing a great number of simple, communicating processors arrayed into a cubical, three-dimensional lattice. Only nearest-neighbor communication among processors is assumed and there is no reliance on global shared memory. The algorithm is similar in spirit to the classical Progressive Refinement Radiosity Method designed for more conventional computers but is not an adaptation of that technique to massive parallelism. Instead, the new algorithm uses a discretization of the wave equation as a local rule for shuttling radiant energy values between processors which correspond to regions of space. A number of example images that were created with an implementation of the algorithm on a Connection Machine are depicted and critiqued.