Irrational speeds of configurations growth in generalized Pascal triangles
type: Item
instance of: scholarly article
title: Irrational speeds of configurations growth in generalized Pascal triangles
zbMATH Open document ID: 0786.68072
DOI: 10.1016/0304-3975(93)90029-S
author: Ivan Korec
published in: Theoretical Computer Science
publication date: 1993-05-24T00:00:00Z
review text: In the introduction the author asks for properties that a one-dimensional cellular automaton should have to simulate waves caused by throwing coins into a \((1-D)\) water-reservoir. A natural condition, as suggested by the author, is that, for a bounded initial configuration, the length of the support grows in linear time and with a speed independent of the initial conditions. The author then introduces generalized Pascal's triangles which give rise to irrational speeds, which are effectively constructed. For this purpose pleasant number-theoretical ideas enter the picture.
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11R99
zbMATH DE Number: 178046
zbMATH Keywords: cellular automata
zbMATH Keywords: Pascal's triangles
zbMATH Keywords: speeds of configurations growth
zbMATH Keywords: algebraic numbers
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
cites work: Computation theoretic aspects of cellular automata
cites work: Q3745840
cites work: Q3753492
cites work: Q5588717
full work available at URL: 0304-3975(93)90029-s
OpenAlex ID: W2078399571
description: scientific article; zbMATH DE number 178046