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On complexity of colloid cellular automata.

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Colloid cellular automata use logical functions from electrical responses of zinc oxide and proteinoids. This study analyzes their space-time complexity, revealing a hierarchy of emergent computational behaviors.

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Area of Science:

  • Computational science
  • Biophysics
  • Materials science

Background:

  • Colloids exhibit complex electrical responses.
  • Cellular automata model systems with local interactions.
  • Boolean circuits represent logical operations.

Purpose of the Study:

  • To derive Boolean circuits from the electrical responses of colloids.
  • To create and analyze colloid cellular automata.
  • To evaluate the space-time complexity of these emergent systems.

Main Methods:

  • Encoding binary strings as electrical potentials and applying them to colloids (ZnO, proteinoids).
  • Recording colloid responses to infer implemented Boolean functions.
  • Mapping functions to cellular automata rules and analyzing space-time complexity using measures like entropy and compressibility.

Main Results:

  • Boolean circuits were successfully extracted from colloid electrical responses.
  • Colloid cellular automata were constructed, exhibiting complex space-time dynamics.
  • A hierarchy of phenomenological and measurable space-time complexity was established.

Conclusions:

  • Colloid electrical responses can be translated into computable Boolean functions.
  • Colloid cellular automata demonstrate emergent complexity from simple rules.
  • This work bridges materials science, computation, and complexity theory.