Three-Colors (BGW or Black-Gray-White) Cellular Automata and Free Will for Artificial Machines

Abstract Instead of the usual 256 rules Cellular Automata (CA) using two bits (black and white), a different type of CA having three symbols (“trits”) and 19,683 possible rules using three different colors (black or 0, gray or 1, and white or 2) is proposed. A score system (with four scores) is discussed, which allows to classify each universe for each different rule into “Blank”, “Pattern”, “One Cycle”, “Complex” or “Unclassified”. This is important because otherwise the overwhelming number of possible universes would make the results intractable. Also, a brief but wide literature review on CA is conducted. The constraint for “allowing” machines to have “free will”, consisting in giving them or denying them stochastic behavior is proposed. Finally, considering the recent advancements concerning Large Language Models (LLMs), the conclusion derived from CA regarding their “free will” is discussed for the case of LLMs and the achievement of Artificial General Intelligence (AGI) in the case of LLMs.