Contents

• Contents
• Introduction
• The Cross Ratio
  • Relative distance interpretation
  • In a plane
  • The state of invariant theory
• Putzer's Method
  • Background
  • The Cayley-Hamilton theorem
  • Reduction of a power series modulo the characteristic polynomial
  • Sylvester's formula
  • A chain of references
• Chaté-Manneville Automata
  • Mapping the mean field probabilities
  • Idempotency as a periodicity criterion
• Reversible Automata
  • Uniform multilplicity
  • Diagrams
  • The matrices
  • Block permutations
• Rule 110
  • Subset diagram
  • Mean field probabilities
  • Gliders in the ether
  • Speed limits
  • Glider collisions
  • Nonemergence of large triangles
• Lorentz Contraction
  • Small matrices
  • Quaternions versus elementary matrices
  • Quaternion inverse
  • Square roots
  • Vector exponential
  • Visualizing products
• Episode I
• Summary
• Bibliography