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Von Neumann's System of Self-Replication Automata with the ability to evolve (Figure adapted from Luis Rocha's Lecture Notes at Binghamton University [6]).i) the self-replicating system is composed of several automata plus a separate description (an encoding formalized as a Turing 'tape') of all the automata: Universal Constructor (A), Universal Copier (B), operating system (C), extra ...
Thus, once a loop is surrounded, it is incapable of reproducing, resulting in a coral-like colony with a thin layer of reproducing organisms surrounding a core of inactive "dead" organisms. The maximum population will be asymptotic to ⌊ A 121 ⌋ {\displaystyle \textstyle \left\lfloor {\frac {A}{121}}\right\rfloor } , where A is the total ...
The general concept of artificial machines capable of producing copies of themselves dates back at least several hundred years. An early reference is an anecdote regarding the philosopher René Descartes, who suggested to Queen Christina of Sweden that the human body could be regarded as a machine; she responded by pointing to a clock and ordering "see to it that it reproduces offspring."
Self-replication is a fundamental feature of life. It was proposed that self-replication emerged in the evolution of life when a molecule similar to a double-stranded polynucleotide (possibly like RNA) dissociated into single-stranded polynucleotides and each of these acted as a template for synthesis of a complementary strand producing two double stranded copies. [4]
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. Nobili's cellular automaton is a variation of von Neumann's cellular automaton, augmented with the ability for confluent cells to cross signals and store information.
Automata theory is closely related to formal language theory. In this context, automata are used as finite representations of formal languages that may be infinite. Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata.
The Von Neumann universal constructor based on the von Neumann cellular automaton was fleshed out in his posthumous Theory of Self Reproducing Automata. [295] The von Neumann neighborhood, in which each cell in a two-dimensional grid has the four orthogonally adjacent grid cells as neighbors, continues to be used for other cellular automata. [296]
The Byl's loop was developed just a few years after Langton's simplification of Codd's automaton, which produced a simpler automaton that would reproduce itself in 151 time-steps. John Byl simplified Langton's automaton further, with an even smaller automaton that reproduced in just 25 time-steps.