Replication in one-dimensional cellular automata

In a cellular automaton (CA), replication is the ability to indefinitely generate copies of a finite collection of patterns, starting from finite seeds. A transparent feature of additive CA, replication mechanisms are less clear in the absence of additivity; this paper investigates such dynamics through several examples. For the 1 Or 2 rule and its generalizations, replication is inevitable and we investigate self-organization properties. In the Perturbed Exactly 1 rule we study frequency of replicators, and the new phenomenon is called quasireplication. The last CA is the Extended 1 Or 3 rule, which allows for replication on different backgrounds. We employ a mixture of rigorous and empirical techniques.