Field Programmable Gate Array Technology as an Enabling Tool Towards Large-Neighborhood Cellular Automata on Cells with Many States

Abstract

Cellular Automata (CA) have been used for many decades to simulate physical processes. From the $3 \times 3$ and $5 \times 5$ neighborhoods of the 1950’s, and typically on binary images, as recently as the mid-2010’s the neighborhoods went up to $15 \times 15$ on images with a few states. Field Programmable Gate Array (FPGA) technology, already applicable to CA simulation since the early 1990’s, has reached such maturity levels that a small device can simulate large-neighborhood CA. In this work we present an architecture which we have fully implemented, that can simulate CA with up to $29 \times 29$ neighborhoods on 256-state cells for Full High Definition (FHD) image input/output with real-time 60 frames-per-second capability. Emphasis of the present work is on the game-changing opportunities that FPGA technology creates to the CA community. We present results from the Greenberg-Hastings and Hodgepodge models, as well as a large-neighborhood anisotropic model. Large neighborhoods either yield qualitatively different results vs. smaller neighborhoods, or lead to results which are merely impossible to produce with small neighborhoods. A comparison of FPGA technology for CA shows advantages vs. conventional Central Processing Units (CPUs) or Graphics Processor Units (GPUs).