# Tile Pattern KL-Divergence for Analysing and Evolving Game Levels

arXiv: https://arxiv.org/abs/1905.05077 · HTML: https://mlsanity.com/paper/1905.05077/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 16 of 16)

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- [Hierarchically Composing Level Generators for the Creation of Complex Structures](https://mlsanity.com/paper/2302.01561/) (2023)
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- [tile2tile: Learning Game Filters for Platformer Style Transfer](https://mlsanity.com/paper/2208.07699/) (2022)
- [Human-Aligned Procedural Level Generation Reinforcement Learning via Text-Level-Sketch Shared Representation](https://mlsanity.com/paper/2508.09860/) (2025)
- [Lode Enhancer: Level Co-creation Through Scaling](https://mlsanity.com/paper/2308.01543/) (2023)
- [Latent Combinational Game Design](https://mlsanity.com/paper/2206.14203/) (2022)
- [Exploring Knowledge Transfer in Evolutionary Many-task Optimization: A Complex Network Perspective](https://mlsanity.com/paper/2407.08918/) (2024)
- [Markov Senior -- Learning Markov Junior Grammars to Generate User-specified Content](https://mlsanity.com/paper/2408.05959/) (2024)
- [Punch Out Model Synthesis: A Stochastic Algorithm for Constraint Based Tiling Generation](https://mlsanity.com/paper/2501.14786/) (2025)
- [Expanding Horizons of Level Diversity via Multi-objective Evolutionary Learning](https://mlsanity.com/paper/2509.24341/) (2025)
- [Learning Local Constraints for Reinforcement-Learned Content Generators](https://mlsanity.com/paper/2605.13570/) (2026)

## Abstract (arXiv)

This paper provides a detailed investigation of using the Kullback-Leibler (KL) Divergence as a way to compare and analyse game-levels, and hence to use the measure as the objective function of an evolutionary algorithm to evolve new levels. We describe the benefits of its asymmetry for level analysis and demonstrate how (not surprisingly) the quality of the results depends on the features used. Here we use tile-patterns of various sizes as features. When using the measure for evolution-based level generation, we demonstrate that the choice of variation operator is critical in order to provide an efficient search process, and introduce a novel convolutional mutation operator to facilitate this. We compare the results with alternative generators, including evolving in the latent space of generative adversarial networks, and Wave Function Collapse. The results clearly show the proposed method to provide competitive performance, providing reasonable quality results with very fast training and reasonably fast generation.