Von Neumann cellular automata are the original expression of cellular automata, the development of which was prompted by suggestions made to John von Neumann by his close friend and fellow mathematician Stanislaw Ulam.
Their original purpose was to provide insight into the logical requirements for machine self-replication, and they were used in von Neumann's universal constructor.
Each state includes the colour of the cell in the cellular automata program Golly in (red, green, blue).
Note that confluent states have the property of a one-cycle delay, thus effectively holding two bits of data at any given time.
The choice of which destination state the cell will reach is determined by the sequence of input signals.
A simple configuration in von Neumann's cellular automaton. A binary signal is passed repeatedly around the blue wire loop, using excited and quiescent
ordinary transmission states
. A confluent cell duplicates the signal onto a length of red wire consisting of
special transmission states
. The signal passes down this wire and constructs a new cell at the end. This particular signal (1011) codes for an east-directed special transmission state, thus extending the red wire by one cell each time. During construction, the new cell passes through several sensitised states, directed by the binary sequence.
The nine cell types that can be constructed in von Neumann's CA. Here, binary signals pass along nine ordinary transmission lines, constructing a new cell when they encounter a ground state at the end. For example, the binary string 1011 is shown on the fifth line, and constructs the east-directed special transmission state – this is the same process as used in the automaton at the top of this page. Note that there is no interaction between neighbouring wires, unlike in
Wireworld
for example, allowing for a compact packing of components.
Roughly 4000 bits of data in a curled up "tape" constructing a complex pattern. This uses a 32-state variation of von Neumann cellular automata known as Hutton32.