# Programmable Cellular Automata

arXiv: https://arxiv.org/abs/2609.06102 · HTML: https://mlsanity.com/paper/2609.06102/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [Large Language Models and Games: A Survey and Roadmap](https://mlsanity.com/paper/2402.18659/) (2024)
- [Level Generation Through Large Language Models](https://mlsanity.com/paper/2302.05817/) (2023)
- [MarioGPT: Open-Ended Text2Level Generation through Large Language Models](https://mlsanity.com/paper/2302.05981/) (2023)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Illuminating Diverse Neural Cellular Automata for Level Generation](https://mlsanity.com/paper/2109.05489/) (2021)
- [Game Generation via Large Language Models](https://mlsanity.com/paper/2404.08706/) (2024)
- [GAVEL: Generating Games Via Evolution and Language Models](https://mlsanity.com/paper/2407.09388/) (2024)
- [Word2World: Generating Stories and Worlds through Large Language Models](https://mlsanity.com/paper/2405.06686/) (2024)
- [Organic Building Generation in Minecraft](https://mlsanity.com/paper/1906.05094/) (2019)
- [The Procedural Content Generation Benchmark: An Open-source Testbed for Generative Challenges in Games](https://mlsanity.com/paper/2503.21474/) (2025)
- [Word2Minecraft: Generating 3D Game Levels through Large Language Models](https://mlsanity.com/paper/2503.16536/) (2025)
- [Mortar: Evolving Mechanics for Automatic Game Design](https://mlsanity.com/paper/2601.00105/) (2025)

## Abstract (arXiv)

Cellular automata is a local computation paradigm where complex behavior can arise from local interactions between simple functions. This paradigm has been used to explain many systems such as biological processes, traffic simulation, computer networks, etc. In games, cellular automata have been used in games such as SimCity and for the generation of spatial content such as caves or dungeons. However, creating effective local rules is hard and unintuitive. Cellular automata can be effectively evolved, but may still be hard to interpret. In this work, we introduce the concept of programmable cellular automata, where we represent the system as Python code. We also modularize the cellular automata into local functions and a decision function. Local functions take a local neighborhood and return a value, while the decision function takes the output of the local functions and decides the value of the next state. Separating the cellular automata into modules written in Python helps with understanding how these systems are working. We also explore adding global functions where they take the whole state and compute a function from it. We tested generating levels for three different games from the PCG Benchmark. The results showed that global functions decrease the number of iterations that cellular automata need to solve a problem, and that we cannot find solutions for some problems with purely local functions. Looking into the generated functions, we can see common functions that have been used in different experiments, which not only helps us understand the generator but also helps us understand these games better and what is important for them.