Contents

• Contents
• List of Figures
• List of Tables
• Overview
  • Introduction
  • Rule 110 as a consequence of triangular tiles
  • Some triangle-induced equivalence relations
  • 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
    • plaid diagram
    • mean field probability
    • two block probability
  • Evolutionary generalities
• The Gliders
  • 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 2c/3
    • 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 -4c/15 ($\approx$ -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 -18c/92 ($\approx$ -c/5)
  • Cook's glider gun, velocity -20c/77 ($\approx$ -c/4).
• Glider Collisions
  • Generalities
    • glider widths and glider parities
    • maps of collision chains
  • Collisions with A gliders
    • the A - B collision vanishes
    • the three A - C collisions
    • A - D collisions
    • A - E collisions
    • An - EBar collisions
    • An - F collisions
  • Collisions with B gliders
    • the three B - C collisions
    • B - D collisions
    • B - F collisions
    • BBar5 - En collisions
  • Collisions with BBar gliders
  • Collisions with C gliders
    • C - D collisions
    • C - E collisions
    • C - F collisions
  • Collisions with D gliders
  • Collisions with E gliders
  • Collisions with F gliders
• Conclusions
  • Acknowledgements
• Bibliography