A reformulated radiosity algorithm is presented that produces initial images in time linear to the number of patches. The enormous memory costs of the radiosity algorithm are eliminated by computing form-factors on-the-fly. The technique is based on the approach of rendering by progressive refinement. The algorithm provides a solution almost immediately which progresses continuously to the complete radiosity solution. In this way the competing demands of realism and interactivity are accommodated. The technique brings the use of radiosity for interactive rendering within reach and has implications for the use and development of current and future graphics workstations. An early software version of the shooting and sorting algorithm described was implemented on a VAX8700 and run on a highly complex scene to test its performance. A model of a steel mill was constructed containing 30,000 patches which were subdivided into 50,000 elements.