Modeling wave propagation using cellular automata on Chip

Abstract

Cellular automata (CA) are often used for physical modelings in which space and time are discrete by assumption. An artificial organism can be considered as a circuit that controls a high-level integrated CA architecture, developed for some mathematical purpose. In this work, propagation and reflection wave phenomenon has been reproduced using CA systems, in a one-dimensional lossless medium. The main objective here was to develop a modeling tool, called vCAgen, which provides the VHDL code for the CA-based system implementation. The CA-based system called CamphslD, composed of 185 cells and two receiver channels, was mapped on a Xilinx Zynq Ultrascale 7EV1156 device, using 27-bit width floating-point arithmetic representation. The proposed CamphslD was effectively mapped on the Zynq device, achieving an operational frequency of 100 MHz and throughput of 25 MOPS. Numerical comparisons allow us to conclude that the proposed CA-system, which is based on simple arithmetic operations, achieves the same results that a reference model based on the well known d'Alembert one-dimensional discrete wave solution, with a Mean Square Error (MSE) in the order of 10−13