The Parallel Substitution Algorithm (PSA) is a spatial dynamical system used to represent processes in cellular space. The PSA is applied to designing programs of self-replication in cellular space. The programs become more laconic (by the number of transition rules or substitutions) in comparison with the ones based on the classic cellular automata model. In this paper, there are presented two PSAs for modelling processes of self-replication of a rectangular loop in a cellular array. The first PSA simulates the self-replication process of the loop in one direction – from left to right. The second one simulates it in two directions – from left to right and from bottom upwards.

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