# Illuminating Diverse Neural Cellular Automata for Level Generation

arXiv: https://arxiv.org/abs/2109.05489 · HTML: https://mlsanity.com/paper/2109.05489/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Open-Ended Learning Leads to Generally Capable Agents](https://mlsanity.com/paper/2107.12808/) (2021)
- [Procedural Content Generation via Machine Learning (PCGML)](https://mlsanity.com/paper/1702.00539/) (2017)
- [Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-Seeking Agents](https://mlsanity.com/paper/1712.06560/) (2017)
- [PCGRL: Procedural Content Generation via Reinforcement Learning](https://mlsanity.com/paper/2001.09212/) (2020)
- [Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space](https://mlsanity.com/paper/1912.02400/) (2019)
- [Differentiable Quality Diversity](https://mlsanity.com/paper/2106.03894/) (2021)
- [Quality-Diversity Optimization: a novel branch of stochastic optimization](https://mlsanity.com/paper/2012.04322/) (2020)
- [Illuminating Mario Scenes in the Latent Space of a Generative Adversarial Network](https://mlsanity.com/paper/2007.05674/) (2020)
- [Learning Controllable Content Generators](https://mlsanity.com/paper/2105.02993/) (2021)
- [Scaling MAP-Elites to Deep Neuroevolution](https://mlsanity.com/paper/2003.01825/) (2020)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Lenia and Expanded Universe](https://mlsanity.com/paper/2005.03742/) (2020)
- [Empowering Quality Diversity in Dungeon Design with Interactive Constrained MAP-Elites](https://mlsanity.com/paper/1906.05175/) (2019)
- [Video Game Level Repair via Mixed Integer Linear Programming](https://mlsanity.com/paper/2010.06627/) (2020)
- [BOP-Elites, a Bayesian Optimisation algorithm for Quality-Diversity search](https://mlsanity.com/paper/2005.04320/) (2020)
- [Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems](https://mlsanity.com/paper/1908.06663/) (2019)
- [Mixed-Initiative Level Design with RL Brush](https://mlsanity.com/paper/2008.02778/) (2020)
- [It's Hard for Neural Networks To Learn the Game of Life](https://mlsanity.com/paper/2009.01398/) (2020)
- [Are Efficient Deep Representations Learnable?](https://mlsanity.com/paper/1807.06399/) (2018)
- [Evolving Structures in Complex Systems](https://mlsanity.com/paper/1911.01086/) (2019)
- [Using Fractal Neural Networks to Play SimCity 1 and Conway's Game of Life at Variable Scales](https://mlsanity.com/paper/2002.03896/) (2020)
- [Self-Referential Quality Diversity Through Differential Map-Elites](https://mlsanity.com/paper/2107.04964/) (2021)

## Built on by (most cited first, 30 of 35)

- [Evolving Curricula with Regret-Based Environment Design](https://mlsanity.com/paper/2203.01302/) (2022)
- [Deep Surrogate Assisted Generation of Environments](https://mlsanity.com/paper/2206.04199/) (2022)
- [pyribs: A Bare-Bones Python Library for Quality Diversity Optimization](https://mlsanity.com/paper/2303.00191/) (2023)
- [Covariance Matrix Adaptation MAP-Annealing](https://mlsanity.com/paper/2205.10752/) (2022)
- [Proximal Policy Gradient Arborescence for Quality Diversity Reinforcement Learning](https://mlsanity.com/paper/2305.13795/) (2023)
- [Learning Controllable 3D Level Generators](https://mlsanity.com/paper/2206.13623/) (2022)
- [Stabilizing Unsupervised Environment Design with a Learned Adversary](https://mlsanity.com/paper/2308.10797/) (2023)
- [DreamCraft: Text-Guided Generation of Functional 3D Environments in Minecraft](https://mlsanity.com/paper/2404.15538/) (2024)
- [Accelerated Quality-Diversity through Massive Parallelism](https://mlsanity.com/paper/2202.01258/) (2022)
- [Path of Destruction: Learning an Iterative Level Generator Using a Small Dataset](https://mlsanity.com/paper/2202.10184/) (2022)
- [The Five-Dollar Model: Generating Game Maps and Sprites from Sentence Embeddings](https://mlsanity.com/paper/2308.04052/) (2023)
- [Goal-Guided Neural Cellular Automata: Learning to Control Self-Organising Systems](https://mlsanity.com/paper/2205.06806/) (2022)
- [Mutation Models: Learning to Generate Levels by Imitating Evolution](https://mlsanity.com/paper/2206.05497/) (2022)
- [Arbitrarily Scalable Environment Generators via Neural Cellular Automata](https://mlsanity.com/paper/2310.18622/) (2023)
- [Surrogate Assisted Generation of Human-Robot Interaction Scenarios](https://mlsanity.com/paper/2304.13787/) (2023)
- [Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometry](https://mlsanity.com/paper/2206.00106/) (2022)
- [Measuring Diversity of Game Scenarios](https://mlsanity.com/paper/2404.15192/) (2024)
- [LatticeWorld: A Multimodal Large Language Model-Empowered Framework for Interactive Complex World Generation](https://mlsanity.com/paper/2509.05263/) (2025)
- [A Unified Substrate for Body-Brain Co-evolution](https://mlsanity.com/paper/2203.12066/) (2022)
- [GriddlyJS: A Web IDE for Reinforcement Learning](https://mlsanity.com/paper/2207.06105/) (2022)
- [Hierarchically Composing Level Generators for the Creation of Complex Structures](https://mlsanity.com/paper/2302.01561/) (2023)
- [Augmentative Topology Agents For Open-Ended Learning](https://mlsanity.com/paper/2210.11442/) (2022)
- [Pathfinding Neural Cellular Automata](https://mlsanity.com/paper/2301.06820/) (2023)
- [Don't Bet on Luck Alone: Enhancing Behavioral Reproducibility of Quality-Diversity Solutions in Uncertain Domains](https://mlsanity.com/paper/2304.03672/) (2023)
- [Start Small: Training Controllable Game Level Generators without Training Data by Learning at Multiple Sizes](https://mlsanity.com/paper/2209.15052/) (2022)
- [Efficient Learning of Locomotion Skills through the Discovery of Diverse Environmental Trajectory Generator Priors](https://mlsanity.com/paper/2210.04819/) (2022)
- [Quality Diversity in the Amorphous Fortress (QD-AF): Evolving for Complexity in 0-Player Games](https://mlsanity.com/paper/2312.02231/) (2023)
- [Multi-Texture Synthesis through Signal Responsive Neural Cellular Automata](https://mlsanity.com/paper/2407.05991/) (2024)
- [Neural Cellular Automata Learn General Features in their Hidden Channels](https://mlsanity.com/paper/2609.21870/) (2026)
- [Evolutionary Machine Learning and Games](https://mlsanity.com/paper/2311.16172/) (2023)

## Abstract (arXiv)

We present a method of generating diverse collections of neural cellular automata (NCA) to design video game levels. While NCAs have so far only been trained via supervised learning, we present a quality diversity (QD) approach to generating a collection of NCA level generators. By framing the problem as a QD problem, our approach can train diverse level generators, whose output levels vary based on aesthetic or functional criteria. To efficiently generate NCAs, we train generators via Covariance Matrix Adaptation MAP-Elites (CMA-ME), a quality diversity algorithm which specializes in continuous search spaces. We apply our new method to generate level generators for several 2D tile-based games: a maze game, Sokoban, and Zelda. Our results show that CMA-ME can generate small NCAs that are diverse yet capable, often satisfying complex solvability criteria for deterministic agents. We compare against a Compositional Pattern-Producing Network (CPPN) baseline trained to produce diverse collections of generators and show that the NCA representation yields a better exploration of level-space.