Rule 110 as it relates to the presence of gliders

Harold V. McIntosh
Departamento de Aplicación de Microcomputadoras,
Instituto de Ciencias, Universidad Autónoma de Puebla,
Apartado postal 461, 72000 Puebla, Puebla, México.

January 29, 1999
revised, Wed Feb 17 19:39:02 GMT-0600 1999

Abstract:

Recent correspondence in LifeMail dealt with the possiblity of ``universal computation'' using Wollfram's (2,1) cellular automaton Rule 110. While awaiting further details participants in the list were referred to an eight page prospectus written by Matthew Cook cataloging the known gliders for the rule. Some of the commentary surrounding his introduction is reproduced and elaborated here, namely the results of the survey of the properties of Rule 110 carried out via the cellular automaton program NXLCAU21.
 

  • Contents
  • List of Figures
  • List of Tables
  • Overview
  • Rule 110 as a consequence of triangular tiles
  • The simplest mosaics according to Rule 110
  • T1 mosaic
  • T2 mosaic
  • T3 mosaic
  • crystallography of the ether tile
  • T4 mosaic
  • T5 mosaic
  • General properties of Rule 110
  • interpretation of graphs
  • the de Bruijn diagrams
  • cycle, or basin, diagrams
  • ancestors and symbolic de Bruijn matrices
  • subset diagram
  • mean field probability
  • Gliders not using the ether tile
  • two right in five generations
  • four left in six generations
  • one left in six generations
  • Cook's A-gliders, with forward velocity 2/3 c
  • tiling approach
  • de Bruijn approach
  • non-existence of (4,6) A-bar gliders
  • Cook's B-gliders, with backward velocity -c/2
  • tiling approach to the B gliders at -2 in 4 generations
  • de Bruijn approach to the B gliders
  • tiling by B-bar gliders at -6 in 12 generations
  • Cook's C gliders, static with velocity 0
  • tiling approach
  • de Bruijn approach
  • Cook's D-gliders, forward velocity c/5
  • Cook's E-gliders, velocity -4/15 c ( -c/4)
  • tiling approach to -4/15 gliders
  • tiling approach to -8/30 gliders
  • Cook's F-glider, backward velocity -c/9
  • Cook's G-gliders, backward velocity -c/3
  • Cook's H-glider, velocity -18/92 c ( -c/5)
  • Cook's glider gun, velocity -20/77 ( -c/4).
  • Glider collisions
  • the A - B collision vanishes
  • an A - C collision makes an F
  • Acknowledgements
  • References
  • About this document ...


    • Harold V. McIntosh

    E-mail:mcintosh@servidor.unam.mx