Soliton-like behavior in automata
type: Item
instance of: scholarly article
title: Soliton-like behavior in automata
zbMATH Open document ID: 0604.68061
DOI: 10.1016/0167-2789(86)90068-0
author: James K. Park
author: Ken Steiglitz
author: William P. Thurston
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: We propose a new kind of automaton that uses newly computed site values as soon as they are available. We call them Filter Automata (FA); they are analogous to Infinite Impulse Response (IIR) digital filters, whereas the usual Cellular Automata (CA) correspond to Finite Impulse Response (FIR) digital filters. It is shown that as a class the FA's are equivalent to CA's, in the sense that the same array of space-generation values can be produced; they must be generated in a different order, however. A particular class of irreversible, totalistic FA's are described that support a profusion of persistent structures that move at different speeds, and these particle-like patterns collide in nondestructive ways. They often pass through one another with nothing more than a phase jump, much like the solitons that arise in the solution of certain nonlinear differential equations. Histograms of speed, displacement, and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide. We then present statistics, for neighborhood radii 2 to 9, which show that collisions which preserve the identity of particles are very common.
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 76B25
zbMATH DE Number: 3976347
zbMATH Keywords: infinite impulse response digital filters
zbMATH Keywords: solitary wave
zbMATH Keywords: Filter Automata
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90068-0
OpenAlex ID: W2008205715
cites work: Q3677181
cites work: Q3677179
cites work: Q3675526
cites work: Q4146660
cites work: Q3944542
description: scientific article; zbMATH DE number 3976347