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Inter- and intracellular computation models based on Boolean vs. non-Boolean inconsistency

Y P Gunji1, H Sadaoka, K Ito

  • 1Department of Earth and Planetary Sciences, Faculty of Science, Faculty of Graduate Science and Technology, Kobe University, Japan.

Bio Systems
|January 1, 1995
PubMed
Summary
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We introduce a novel model for non-computable systems, merging intracellular and intercellular computation. This cellular automata model reveals hierarchical structures and undecidability at the edge of chaos.

Area of Science:

  • Computational Biology
  • Theoretical Computer Science
  • Complex Systems

Background:

  • Intracellular and intercellular computations present challenges in defining system computability.
  • Existing models often struggle to capture the complexities of systems with both internal and external computational processes.

Purpose of the Study:

  • To propose a computational model for systems exhibiting both intracellular and intercellular computation.
  • To investigate the emergence of non-computability and hierarchical structures in such systems.
  • To explore the relationship between Boolean and non-Boolean logic in complex systems.

Main Methods:

  • Development of a cellular automata model incorporating an inconsistent relation between Boolean and non-Boolean logic.
  • Analysis of system evolution, particularly its location at the edge of chaos (Class 4).

Related Experiment Videos

  • Investigation of the absence of a universal local rule governing the entire system space.

    • Main Results:

    • The model demonstrates evolutionary behavior akin to Class 4 systems, operating at the edge of chaos.
    • No single local rule was found to ensure universality across the entire system.
    • The system, characterized by an inconsistent vertical scheme, approximates a hierarchical structure.
    • Undecidability between system parts and the whole is a key feature, defining its hierarchical nature.

    Conclusions:

    • Systems with integrated intracellular and intercellular computation are inherently non-computable.
    • The proposed model elucidates how hierarchical structures and undecidability arise from the interplay of different logical systems.
    • The findings suggest that the wholeness of such complex systems cannot be predicted from local rules alone.