The Cellular Automata of John von
Counters and buffers
Counters, more precisely n-counters, serve mostly to provide the timing of automaton processes. An n-counter is an organ that releases a pulse just after receiving n sparse pulses.
The figure here below shows four n-counters with n = 2, 3, 4, 5.
These simple organs exploit the
property that a vacuum state activated by a single pulse evolves spontaneously towards a quiescent ordinary transmission state (right
blue-arrow) through a sequence of sensitized states.
Therefore, if n sparse enough pulses propagate
along a horizontal transmission
line with n
gaps (missing arrows), just n
input pulses are needed to bridge all gaps, thus letting any further input-pulse
to reach the output line. Since filling a one-cell gap through a sequence of sensitized states lasts 4 or 5 time steps, it is clear that the pulses are sparse enough if they are spaced by more
than 5 quiescent states. If we
want that only one pulse is released at output every n
input pulses, the organ must be provided by a
self-resetting device. This can be formed
by one or more special
transmission states (red
arrows) activated by the first pulse
arriving to output. In fact, the pulses released by
the red arrows annihilate the
bridging arrows, thus restoring the n gaps.
The figure here below
shows a self-resetting 5-counter provided with an input line for external resetting.
The external resetting restores all
gaps independently of whether they are bridged or not. You can find several examples of working counters in the automaton-file
It is quite evident that cellular
automata capable of performing complex operations need memory devices. There are several ways to
implement memories capable of
storing n binary digits (n-bit buffers). The universal constructor UC_REP_UNITS.JVN
contains five 1-bit buffers working (also in the EVN enviroment) as shown in the figure here below.
In A, an input
pulse activates a 5-pulse coder resulting in the activation of a small buffering circuit, as shown in A'. The
buffering circuit includes a confluent
state and an ordinary transmission state pointing to a second confluent
state. In B, an input pulse activates a
6-pulse coder, which annihilates the active confluent state and creates immediately a quiescent confluent state. This operation
inactivates the buffering circuit. C, C' and D, D' show a 1-bit reading
process that uses a confluent state as a logical
AND. The next figure shows a 1-bit buffer working only in the EVN
The device has two inputs and one
output. One of the two inputs is used to store the bit, the other to read the memory content (0 or 1).
The bit 1 is stored as an excited
confluent state (orange diamond). After the reading process,
the memory content is
automatically reset to 0 (gray diamond). In A, a pulse enters
the reading line. In A', since the
stored bit is 0, no pulse is released. In B, a pulse
enters the writing line. This operation results to the excitation of
the confluent state (orange diamond). In C, a pulse
enters the reading line. In C', since
the stored bit is 1, a pulse is released.
The next figure shows a
5-bit buffer working only in the EVN environment. It collects a sequence of 5-bit sequence formed
by zeros and ones sparsely inputted
one by one to lines 0 and 1 respectively. These bits are sent both to a
5-counter and to an
organ called the collector where are stored as excitation levels in an array of spaced confluent states, as detailed after the next figure. The bits pass then to a second confluent-state
array and recovered from here as
an activation train by a suitable procedure.
The first bit 0 or 1 is stored as an
unexcited or excited level of the first confluent state of
collector. Whenever a new bit
arrives, the array of bits shifts
one step right, so that the bit can be in turn stored in the first confluent state just freed. Therefore, the collector behaves as a shift
register. The shift is caused by the creation of a
temporary set of right blue-arrows in the inter-spaces of the confluent-state array, what is done
by the red arrows under the
action of an activation train generated by coder c1. As soon as just 5
bits are collected, the counter
releases a pulse that starts coder c2,
which generates an activation train that makes the red arrows create a transitory set of down blue-arrows. This operation produces
the transfer of the excitation levels
from the first to the second confluent-state array. Since these
confluent states are in touch
with a left blue-line, the excitation levels are immediately collected by this line and sent away as an activation train. The organ just described
is available in 5-BIT_BUFFER.EVN and the fragment-file 5-BIT_BUFFER.EFR.
The next figure shows a
6-bit buffer (working only in EVN) where the counter
is replaced by an external control
R that starts, through coder c1, the release of the collected bit sequence.
The device also releases the
rightmost stored bit whenever a new sparse bit is inputted, thus providing a sort of delayed
output. This organ is available in the fragment file 6-BIT_BUFFER.EFR.