Particle graphics simulations are well suited for modeling phenomena such as water, cloth, explosions, fire, smoke, and clouds. They are normal realized in software, as part of an interactive graphics application, such as a video game. Their use in such applications is limited by the computational burden and resource competition they create for a host application. We present the design of a Hardware Particle Machine, for implementation in an FPGA, intended for accelerating real-time particle graphics in applications such as video games. The Particle Machine is a system that completely contains, manages, and executes particle graphics simulations and rendering. The Particle Machine is a system comprised of particle memory, a controller, and the Particle Pipe, a pipelined Particle Update Processor. The Particle Pipe has been synthesized to 130 MHz, on an Altera Stratix FPGA, resulting in a potential throughput of 2.1 million PPF (particles per frame). This throughput is achieved with minimal load on application and main system performance.