Wave Function Collapse in Deep Convolutional Generative Adversarial Network

1. Abstract

The procedural content generation algorithms are a well-known concept in the game industry. Because of their time efficiency, there is more effort put into developing new algorithms. The Wave Function Collapse algorithm developed by Max Gumin is populating the pattern from a small sample. The algorithm gained much popularity because of the variety of the outputs generated from only one input. This paper examines whether the wave function collapse can be trained within a use of Deep Convolutional Generative Adversarial Network to get the output starting with the input specified by the user. This would give additional control over the algorithm and allow to specify the spatial distribution of tiles across the solution space.

Keywords: Wave Function Collapse, Procedural City Generation, Machine Learning, Generative Adversarial Network

Table of contents

Abstract

Acknowledgement

1. Introduction

1.1 The aim of the project

1.2 The structure of the document

1. Background

2.1 Wave Function Collapse

2.2 Artificial Intelligence application to Wave Function Collapse

2.3 Algorithmic Complexity

2. Approach 1: Generative Adversarial Networks

2.1. Introduction

2.2. Dataset preparation

2.3. Image encoding

2.4. Image-to-image translation

2.5. Image post-processing

2.6. Evaluation of results

3. Approach 2: Modification of probability and entropy

3.1. Introduction

3.2. Input image

3.3. Result measurement

3.3.1. Linear mapping based on the lowest and the highest weight

3.3.1. Exponential growth

3.3.2. Enforcing the patterns building desirable content

3.4. Entropy

4. Results

5. Conclusion

6. Appendices

7. References

List of figures

Figure 1 Something something

Figure 2 On the left: Input image that indicates areas with specific desirable values, on the right: the solution that corresponds to the input image

Figure 3 Examples of the 2D patterns generated by Max Gumin with a use of WFC

Figure 4 Island generated with Wave Function Collapse in Bad North