An automata able to reproduce itself, i.e. to produce a copy of itself after a number of transformations.
The project of a self-reproducing cellular automata was initially formed by J.von NEUMANN.
Self-reproduction in a cellular automata is clearly different from self-reproduction in the autopoietic sense, whose models were established later. However, both are obviously related.
It is debatable if the appearance of a "copy" of the initial automata in some other region of the substrate is equivalent to the endogenous self-reproduction of a system endowed with organizational closure.
H. MATURANA states: "Cells do not construct other cells, they just divide into two of the same kind, like in the fragmentation of a crystal" (1979, p.25)
A von NEUMANN automaton would be self reproducing as a whole in a limited sense only if, after a number of operations (through a process akin to an hypercycle), it would regenerate itself The automaton would then comprise the whole cycle.
Otherwise self-reproduction would mean production of another automata of the same type, and eventually of many other ones.
It is however possibly a matter of levels. Self-reproduction of the elements (in the sense of cellular automata) could conceivably lead to the self-reproduction of the complex system (in the sense of autopoiesis)
P. GREUSSAY comments: "von NEUMANN thought that, with a convenient programming of some cellular surface, some group of cell with proper characteristics would be able �to produce a copy of itself in another zone of the cellular surface, this copy being able in turn to do the same" (1988, p.1321)
To achieve his goal, von NEUMANN selected a complex repertory of 29 possible states combined with an intricated transition function.
"In 1968 Edgar CODD� discovered a universal constructor configuration whose cells are limited to 8 different states.
"In 1984 Christopher LANGTON (University of Michigan)�showed that a self-reproductive cellular automata does not necessarily nee the intervention of a cell configuration endowed with the property of a universal constructor" (Ibid, p.1322).
In von NEUMANN, CODD and LANGTON's cellular automata "the self-reproduction process is actively directed by the initial configuration itself, through a transition function. Take an initial configuration at random and there is no more any self-reproduction. Thus such a self-reproduction mechanism requires a quite complex and substantially precise construction. Indeed, to endow the parent structure with the capacity to actively direct its own duplication, transcription devices of the "genetic material" of the initial configuration are needed, as well as translation devices acting on the environmental cellular surface".(p.1322)
We are coming thus very close to organizational closure in autopoiesis.
This research promises to be highly significant for the logic of future complex computers and probably also for genetics.