| The Cellular Automata of John von Neumann
Logical operations and cabling
- The logical operation OR
- The logical operation AND
- OTS-line bifurcations and trifurcations
- Signal termination
- Signal transfer from OTS lines to STS lines
- OTS-line crossings (only for EVN automata)
- Delay lines
The logical operation OR
The logical operation AND
OTS lines pointing to a confluent state can be arranged in ways suitable for the implementation of the logical operator AND. This acts on the binary digits 0, 1 as follows: 0 AND 0 = 0; 1 AND 0 = 0; 1 AND 1 = 1. The operation is commutative, i.e. x AND y = y AND x, and associative, i.e. (x AND y) AND z = x AND y AND z.
OTS-line bifurcations and trifurcations
Confluent states with one departing OTS or STS line are used for activation train bifurcations or trifurcations.
Activation trains propagating along OTS (STS) lines are annihilated (stopped) by a reversed OTS (STS).
Signal transfer from OTS lines to STS lines
Confluent states can be used to transfer activation trains from OTS lines to STS lines. Since active OTSs and active STSs annihilate each other, and active STSs also annihilate the confluent state, the transfer of activation trains can take place only from OTS lines to STS lines.
OTS-line crossings (only for EVN automata)
Cellular automata capable of performing complex functions require very often the crossing of activation trains. In the JVN automata environment, it is impossible to implement the crossing function by an assembly of quiescent cells. Active crossing configurations do exist, but unfortunately, no constructing automaton can generate them, as the creation of active cells alters unpredictably the construction process. The only way to cross two activation trains is by using coding-decoding procedures. The crossing function, however, can be easily implemented by providing the confluent state with three new excitation levels, as implemented by the Author in the EVN transition rules. The figure above shows a crossing configuration of the confluent state in the EVN environment.
Very often, a cellular automaton requires a precise timing of local events, for instance the arrival in coincidence of activation pulses converging to a given cell. The easiest way to accomplish this is by adjusting the length of one or more transmission lines. Since the length of a transmission line with fixed ends can change only by a pair of transmission states, also the insertion of one or an odd number of confluent states into an OTS line is often necessary.