On complexity of colloid cellular automata

TL;DR

This paper investigates the space-time complexity of colloid-based Boolean circuits and their mapping to cellular automata, revealing a hierarchy of phenomenological and measurable complexities through various analytical measures.

Contribution

It introduces a method to extract Boolean functions from colloids and analyzes their corresponding cellular automata complexity using multiple metrics.

Findings

Discovered Boolean functions from colloid responses to electrical stimuli.

Mapped colloid responses onto cellular automata rules.

Established a hierarchy of complexity based on multiple measures.

Abstract

The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from the colloids. We analyse the space-time complexity of Boolean circuits derived from the electrical responses of colloids: ZnO (zinc oxide, an inorganic compound also known as calamine or zinc white, which naturally occurs as the mineral zincite), proteinoids (microspheres and crystals of thermal abiotic proteins), and combinations thereof to electrical stimulation. To extract Boolean circuits from colloids, we send all possible configurations of two-, four-, and eight-bit binary strings, encoded as electrical potential values, to the colloids, record their responses, and thereby infer the Boolean functions they implement. We map the discovered functions onto the cell-state transition rules of cellular automata (arrays of binary state machines that update their states synchronously according to the same rule) -- the colloid cellular automata. We then analyse the phenomenology of the space-time configurations of the automata and evaluate their complexity using measures such as compressibility, Shannon entropy, Simpson diversity, and expressivity. A hierarchy of phenomenological and measurable space-time complexity is constructed.