Large-scale Cellular Automata on FPGAs

Abstract

Cellular automata (CA) are discrete mathematical models discovered in the 1940s by John von Neumann and Stanislaw Ulam and have been used extensively in many scientific disciplines ever since. The present work evolved from a Field Programmable Gate Array– (FPGA) based design to simulate urban growth into a generic architecture that is automatically generated by a framework to efficiently compute complex cellular automata with large 29 × 29 neighborhoods in Cartesian or toroidal grids, with 16 or 256 states per cell. The new architecture and the framework are presented in detail, including results in terms of modeling capabilities and performance. Large neighborhoods greatly enhance CA modeling capabilities, such as the implementation of anisotropic rules. Performance-wise, the proposed architecture runs on a medium-size FPGA up to 51 times faster vs. a CPU running highly optimized C code. Compared to GPUs the speedup is harder to quantify, because CA results have been reported on GPU implementations with neighborhoods up to 11 × 11, in which case FPGA performance is roughly on par with GPU; however, based on published GPU trends, for 29 × 29 neighborhoods the proposed architecture is expected to have better performance vs. a GPU, at one-10th the energy requirements. The architecture and sample designs are open source available under the creative commons license.