| The Cellular Automata of John von Neumann
The constructing arm
The constructing arm (C-arm) is an extensible organ capable of elongating or retracting horizontally or vertically, creating cell states by vacuum state excitation and possibly releasing an activation pulse. As shown in the figure above, it consists of two adjacent transmission lines: one of special transmission states (red arrows) and the other of ordinary transmission states (blue arrows). In some implementations, the red and the blue lines are interchanged. At the C-arm head (H), the terminal arrow of the blue line points to the terminal arrow of the red line. In this configuration, the two lines can mutually annihilate their terminal arrows, add to each other new terminal arrows or create neighboring cell-states. These properties are necessary to implement the activity of the arm. The two lines receive inputs from suitable control organs (not shown in the figure) formed by coders, decoders and various delay lines, which generate activation trains that propagate via lines A, B, then along the C-arm lines up to the arm head, where they promote the arm activity. These activation trains make the C-arm move forwards or backwards step-by-step through empty regions of the cell lattice thus reaching and possibly changing any cell state on the right-top of C-arm origin (O).
How the C-arm works
The files mentioned in the next paragraphs show the basic C-arms operations in detail. By activating the input line of a coder, you can make the C-arm move left, right, up or down by one step, or create a cell-state through the excitation of a vacuum state. The red arrows near coder's inputs indicate the move directions. The arm cannot move right if the previous move was vertical, or down if it was horizontal. As a rule, a C-arm should elicit from the vacuum only quiescent cell states to avoid possible damage. The arm, however, must be able to release an activation pulse to a previously created cell-state, if this needs activation.
C-arm for JVN automata
The file C-ARM_CONTROLS.JVN in folder JVN shows a C-arm provided with a complete set of controls working in the JVN environment. To start the basic actions (go right, go left, go up, go down), activate the corresponding input-lines of the 4 small coders (starters) at the C-arm left, and then run the automaton in mode Walk (button ). You will see the starter to generate an activation train that branches out into four decoders, which work as recognizers. The pulse generated by each decoder is then sent to a pair of coders, which in turn generate two coordinated activation trains that feed the C-arm doublet for arm moves.
C-arm for EVN automata
The file C-ARM_CONTROLS.EVN in folder EVN contains a C-arm workink in the EVN environment. Here, thanks to the crossing function of the confluent state, the input-line activation does not need a multiplexing procedure to command the release of specific activation trains that command the C-arm actions.