Abstract
The parallel substitution algorithm, which is a spatial model for representing fine-grained parallel computations, is used for constructing self-replicating structures in a cellular space. The use of this model allows one to create more compact (in terms of the number of cell states and transition rules) and structured self-reproduction programs compared to the classical cellular automaton model. Two parallel substitution algorithms for modeling the self-reproduction of a cellular structure having the shape of a rectangular loop are presented. One of them models the self-reproduction of the original structures from left to right, and the other, from left to right and from bottom to top.
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