| The Cellular Automata of John von Neumann |
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Switches
On-off switches
On-off switches are devices capable of stopping and restoring the ability of an OTS line (blue-arrow line) to carry activation trains. A way to implement an on-off switch is, for instance, by changing the direction of an arrow of the OTS line so as to exploit the property that two opposite arrows of same color cannot transmit to each other their excitation. Changing the direction of a blue arrow requires that the arrow is first annihilated to a vacuum state, which is in turn replaced by a differently oriented blue-arrow through a sequence of sensitized states. Both operations can be done in sequence by a special transmission state (STS, red arrow) inputted by a suitable activation train. The figure here below shows how a red arrow in tough with a confluent state fed in series by two small coders can switch on or off a horizontal transmission line.
On the left, a pulse inputted to the first coder results to the inversion of the blue arrow pointed to by the red arrow. On the right, the second coder restores the original direction of the blue arrow. Load the automaton-file SIMPLE_SWITCHES.EVN or the fragment-file SIMPLE_SWITCHES.EFR to analyze in detail the behavior of various switches.
Toggle-switches
A toggle-switch is a switch that can be set on or off by a pulse inputted to the same line. One can implement this simple device in various ways, for instance by exploiting the logical AND properties of the confluent state inserted into an OTS line. The figure here below illustrates the simplest example of this sort of switch.
A single pulse released by the red arrow suffices to produce the immediate transition vacuum state ® right blue-arrow or right-blue arrow ® vacuum state, thus switching on or off the vertical transmission line. Unfortunately, the device cannot be so simple in configurations where the stopping blue-arrow cannot be right-oriented. The next figure shows how the logical AND property can be exploited to send single pulses to either output lines, alternatively.
In A, the down red-arrow activated by the input pulse annihilates the right blue-arrow on the output line above just after the pulse has passed, while the up red-arrow creates a right blue-arrow on the output line below. In B, the red arrows do the contrary. The files TOGGLE_SWITCHES.JVN, TOGGLE_SWITCHES.EFR and TOGGLE_SWITCHES.EVN contain a few examples of toggle-switches.
Changeover switches
The changeover switches are simple organs that run the propagation of an activation train from a transmission line to another. They work about as the on-off switches: Two small coders provide the activation trains for the annihilation of a blue arrow and the creation of a differently oriented blue arrow. The figure here below shows a changeover switch in an upward and in a rightward transmission state.
On the top, the pulse entering the coder above annihilates the up blue-arrow and creates a right blue-arrow. On the bottom, the pulse entering the coder below annihilates the right blue-arrow and creates an up blue-arrow. Load the file CHANGEOVER_SWITCHES.EVN to watch two changeovers at work.
