LOGOS-CA: A Cellular Automaton Using Natural Language as State and Rule

TL;DR

LOGOS-CA proposes a framework to run cellular automata where cell states and update rules are expressed in natural language and updated by LLMs, leveraging the expressive power of language to extend CA beyond fixed numeric states. The authors validate the approach with forest-fire and ALife experiments, showing that explicit-rule simulations can be faithfully reproduced by capable LLMs, while flexible descriptions lead to model-dependent dynamics and emergent symbolic states in some models. The results highlight the importance of selecting an appropriate LLM and controlling the degree of rule flexibility when using language-based CA. The work points to broad future applications in chemistry, materials science, traffic, and socio-economic simulations, while also cautioning about interpretability and bias introduced by the language model.

Abstract

Large Language Models (LLMs), trained solely on massive text data, have achieved high performance on the Winograd Schema Challenge (WSC), a benchmark proposed to measure commonsense knowledge and reasoning abilities about the real world. This suggests that the language produced by humanity describes a significant portion of the world with considerable nuance. In this study, we attempt to harness the high expressive power of language within cellular automata. Specifically, we express cell states and rules in natural language and delegate their updates to an LLM. Through this approach, cellular automata can transcend the constraints of merely numerical states and fixed rules, providing us with a richer platform for simulation. Here, we propose LOGOS-CA (Language Oriented Grid Of Statements - Cellular Automaton) as a natural framework to achieve this and examine its capabilities. We confirmed that LOGOS-CA successfully performs simple forest fire simulations and also serves as an intriguing subject for investigation from an Artificial Life (ALife) perspective. In this paper, we report the results of these experiments and discuss directions for future research using LOGOS-CA.

Figures (9)

• Figure 1: Results of forest fire emulation using LOGOS-CA. The top row shows the result of a standard simulation (Reference). Below it are the emulation results for GPT-4o-mini, GPT-4o, GPT-5-nano, GPT-5-mini, and GPT-5. GPT-4o and GPT-5 perfectly emulated the simulation, while GPT-5-mini overall matches Reference despite rarely producing invalid outputs. In contrast, GPT-4o-mini and GPT-5-nano failed to emulate the simulation as early as $t=1$.
• Figure 2: Results of Run 1 for GPT-5-nano in the ALife experiment. The top row (Global color space) shows cells colored by reducing the description embeddings to three dimensions using PCA and linearly mapping each dimension to RGB values. The bottom row (cluster-based) shows cells colored by clustering the L2-normalized embeddings using KMeans with $k=20$, after reducing the dimensionality using PCA until the cumulative contribution reached $95$%.
• Figure 3: Results of Run 1 for GPT-5-mini in the ALife experiment. The top row (Global color space) shows cells colored by reducing the description embeddings to three dimensions using PCA and linearly mapping each dimension to RGB values. The bottom row (cluster-based) shows cells colored by clustering the L2-normalized embeddings using KMeans with $k=20$, after reducing the dimensionality using PCA until the cumulative contribution reached $95$%.
• Figure 4: Field mean (solid line) and $\pm1$ standard deviation (shaded band) of description changes between steps for each cell in the ALife experiment. The left column shows GPT-5-nano and the right column shows GPT-5-mini, with Runs 1–3 shown from top to bottom. For GPT-5-mini, the mean change decreases rapidly before step $20$ and then asymptotically approaches $0$, whereas GPT-5-nano generally maintains relatively high values for both mean and standard deviation.
• Figure 5: Transitions in the counts of symbolic state definitions for GPT-5-nano in the ALife experiment. Runs 1–3 are shown from top to bottom. Single characters (uppercase letters, lowercase letters, and the asterisk) interpreted as states were detected from cell descriptions using the patterns in Table \ref{['tab:patterns']}, and the number of cells (Count) for each character was aggregated and plotted at each step (horizontal axis: Step).