John von Neumann's Cellular Automata | Embryo Project Encyclopedia

# John von Neumann's Cellular Automata

Published: **2010-06-14**

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John von Neumann’s Cellular Automata

Cellular automata (CA) are mathematical models used to simulate complex systems or processes. In several fields, including biology, physics, and chemistry, CA are employed to analyze phenomena such as the growth of plants,
DNA evolution, and
embryogenesis. In the 1940s
John von Neumann formalized the idea of cellular automata in order to create a theoretical model for a self-reproducing machine. Von Neumann’s work was motivated by his attempt to understand biological evolution and self-reproduction.

In 1948, von Neumann set out to describe a model of a self-reproducing machine in a paper called “The General and Logical Theory of Automata” that he wrote for the Hixon Symposium. He had not yet conceived of cellular automata and could not completely solve the problem of how, in theory, a machine could self-reproduce. Only after the suggestion by his colleague
Stanislaw Ulam to use a cell-based concept, was von Neumann able to formulate a model for a machine that was fully capable of self-reproduction. This theoretical model is based on the concept of cellular automata. Von Neumann describes it in his book
_Theory of Self-Reproducing Automata_, which was completed and published after his death by Arthur Walter Burks in 1966.

A cellular automaton is a theoretical machine that consists of elements called cells. Each cell has a value, or state, and is connected to certain neighboring cells so that they form a one- or multidimensional lattice. The states of the cells change at discrete time-steps. The new state of a cell is computed from the previous states of the connected neighboring cells using predefined rules. In _Theory of Self-Reproducing Automata_, von Neumann described a cellular automaton with twenty-nine possible states for each cell and in which every cell is connected to the cell above, below, left, and right (called a “von Neumann” neighborhood). He proved that the dynamics exhibited by such a cellular automaton are similar to the biological processes involved in self-reproduction and evolution. Other cellular automata were developed, for instance by
Edgar Frank Codd in 1968, with different numbers of possible states, connected neighbors, and the rules used to calculate new states.

In his first model of a self-reproducing machine, described in 1948, von Neumann dealt with the information in the model in two ways. First, the information was interpreted by the self-reproducing machine and used as instructions to build a copy of the machine. Second, the information was not interpreted but was copied and given to the newly built machine. This handling of information is analogous to the use of DNA in the reproduction process of living cells. To replicate itself, a living cell copies the DNA and then uses the DNA as instructions to create a new cell via cell division, while the copy of the DNA is given to the new cell. Remarkably,,vo

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