Automata that Construct as well as Compute

In Section 7.1, we introduce the notion of a cellular (or tessellation) automaton, and show how to embed CT-machines within the cellular array. These have the computational power of Turing machines (thus the T) as well as the ability to Construct other CT-machines (thus the C). We then prove results about universal constructors and self-reproducing machines. In Section 7.2, we further formalize the notion of cellular automata, and prove that there exist Garden-of-Eden configurations that cannot arise in the cellular array without intervention of an external agency. Finally, Section 7.3 discusses differences between the type of self-reproduction formalized here and the growth processes of embryology.