Autopoietic Networks

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2024-10-09 02:00:03

A type of cellular automaton based on the concept of autopoiesis is explored, as introduced by Maturana and Varela in Autopoiesis and Cognition: The Realization of the Living, and also a bit developed on in Principles of biological autonomy(1979) by Varela.

Autopoiesis can be viewed as the capacity of an organism to maintain organizational closure or closure of constraints. These very briefly mean that any process (and respective constraints on it) needs to generate atleast another constraint. Here, processes and relations between them evolve in order to maintain such closure. Through this lens, any new adaptation or behaviour taken by an organism can be seen as a compensation to a pertubation (i.e. self-replication).

A network with N x N units is initialized, with each unit’s state $∈ { 0, 1 }$ being randomly assigned. Over each iteration (with a max of N_iter), there’s a logic gate randomly chosen from a set (examples with AND, OR and XOR), for the update of each unit’s state according to its neighbors’ states (extended option to also include neighbors in the diagonals).

If a unit maintains its state after an iteration, regardless of its neighbors, its $\Phi$ value (which is supposed to mimick closure) increases by 1. Moreover, if the states respective to consecutive iterations are different, $\Phi$ is reset to 0. If $\Phi \geq \epsilon$, then the neighbors take the value of the main unit’s state, and an ensemble is formed. With regard to this, $\epsilon$ can be fixed (fix = True) or evolve over time (fix = False) with