Level Generation with Constrained Expressive Range

TL;DR

This work treats the expressive range as a conceptual space of potential game levels and advances a constrained, pattern-guided traversal to explore underrepresented regions defined by density $D$ and difficulty $H$. It leverages a Sturgeon-based constraint generator together with tile-pattern templates learned from seed Mario levels to systematically sample the expressive range, rather than relying on random generation. Key contributions include a sampling pipeline over expressive-range cells, an analysis of how different pattern templates affect coverage and solve-time, and insights into the strengths and limitations of constraint-based exploration for level design. The approach supports more diverse, interesting levels and offers a pathway for curated training data and deeper understanding of generative pipelines in procedural content generation.

Abstract

Expressive range analysis is a visualization-based technique used to evaluate the performance of generative models, particularly in game level generation. It typically employs two quantifiable metrics to position generated artifacts on a 2D plot, offering insight into how content is distributed within a defined metric space. In this work, we use the expressive range of a generator as the conceptual space of possible creations. Inspired by the quality diversity paradigm, we explore this space to generate levels. To do so, we use a constraint-based generator that systematically traverses and generates levels in this space. To train the constraint-based generator we use different tile patterns to learn from the initial example levels. We analyze how different patterns influence the exploration of the expressive range. Specifically, we compare the exploration process based on time, the number of successful and failed sample generations, and the overall interestingness of the generated levels. Unlike typical quality diversity approaches that rely on random generation and hope to get good coverage of the expressive range, this approach systematically traverses the grid ensuring more coverage. This helps create unique and interesting game levels while also improving our understanding of the generator's strengths and limitations.

Figures (8)

• Figure 1: Sliding window horizontally across the level 1-1 of Super Mario Bros. to create the training set.
• Figure 2: Pattern templates. The blue tiles are "input" tile locations, and the purple are "output" tile locations; a certain input tile constrains the corresponding output tiles to be those that were seen in the example level(s). Note that diamondring and block2 jointly constrain the output tiles all at once, while nbr-plus constrains each output tile independently.
• Figure 3: Density-difficulty expressive range of expanded corpus with each pattern template. The color bar is based on SymLogNorm allowing linear behavior around zero and logarithmic beyond.
• Figure 4: Scatter plot displaying the (normalized) interestingness of generated levels across the expressive range, with the size and color of each point reflecting its level of interestingness. Uncolored points represent levels from the initial corpus in extended corpuses.
• Figure 5: Visual exploration of initial levels of the corpus and the generated levels with different pattern templates.