Design of rules

To get an idea of how to use some of the features of the LCAU programs, consider the exercise of designing a binary counter for a (4,1) automaton. The reason for choosing a quaternary automaton is that the two states of the counter, ``0'' and ``1'', can occupy two states of the automaton, the quiescent background another, with one more state left over to represent a carry; this state can be mobile---a glider.

This automaton can be devised using the line editing portion of the main menu, in interaction with the rule display occupying its niche in the same menu.

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• The counter itself
  • Infrastructure
    • quiescent background
    • first bistable state - ZERO
    • left running glider - CARRY
    • second bistable state - ONE
  • Binary arithmetic
    • flip ZERO, absorb CARRY
    • flip ONE, propagate CARRY
  • Packing bistable cells
    • Gap between like cells
    • Gap between unlike cells
  • Carry generator
    • a glider gun
  • Protecting the components
    • protection of phase 22
    • protection of phase 13
    • protection of phase 11
    • some additional protection
• Table of transitions
• Using the line editor
  • Position cursor
  • Enter state
  • Maintainance of the line panel
  • Defining transitions
  • Trial evolution
  • Consistency
  • Prescribed evolution

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Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx