Time reverse automata patterns generated by Spencer-Brown's modulator: invertibility based on autopoiesis

Area of Science:

• * Theoretical Biology
• * Systems Theory
• * Computational Science

Background:

• * Autopoiesis describes self-producing and self-maintaining systems.
• * Existing models often lack explicit temporal dynamics.
• * Spencer-Brown's concept of time provides a foundation for temporal extension.

Purpose of the Study:

• * To introduce explicit time into autopoietic systems.
• * To define autopoietic time and its relationship with self-consistency.
• * To explore time reversibility in the context of cellular automata.

Main Methods:

• * Explicitly introducing time into the framework of autopoiesis.
• * Segregating the definition of time into syntactic and semantic components.
• * Formalizing the relationship between time and self-consistency.
• * Applying the framework to cellular automata and one-to-many mappings.

Main Results:

• * A novel definition of autopoietic time is proposed.
• * Time reversibility is formalized through the link between time and self-consistency.
• * The dynamics of autopoietic systems are extended.
• * An irreversible-like autopoietic time is demonstrated without invoking entropy.

Conclusions:

• * Autopoietic systems can be dynamically extended with an explicit temporal component.
• * The proposed autopoietic time offers a new perspective on system dynamics.
• * This framework provides a basis for understanding complex systems with emergent temporal properties.