Skip to main content

A Multi-agent Sudoku Through the Wave Function Collapse

  • Conference paper
  • First Online:
Multi-Agent Systems (EUMAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14282))

Included in the following conference series:

  • 396 Accesses

Abstract

Sudoku is a logic puzzle that involves filling a 9 \(\times \) 9 grid with digits from 1 to 9 without repeating any number in the same row, column, or subgrid. Translating this traditional newspaper puzzle into a video game raises technical challenges as generating a complete and valid grid, creating puzzles with solutions based on the difficulty level, and implementing user interaction mechanisms. This research paper presents the specification and implementation of Sudoku as a video game using the entropies from the wave function collapse technique and a multi-agent game development methodology. The main focus of the development is to consider each of the 81 cells as autonomous agents, computing the possibilities space for each agent and establishing the information transfer mechanisms based on the game’s constraints.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chover, M., Marín-Lora, C., Rebollo, C., Remolar, I.: A game engine designed to simplify 2D video game development. Multimed. Tools Appl. 79, 12307–12328 (2020)

    Article  Google Scholar 

  2. Danbaba, A.: Construction and analysis of samurai sudoku. Int. J. Math. Comput. Sci. 10(4), 165–170 (2016)

    Google Scholar 

  3. Felgenhauer, B., Jarvis, F.: Mathematics of sudoku I. Math. Spectr. 39(1), 15–22 (2006)

    Google Scholar 

  4. Gumin, M.: Wave Function Collapse: Bitmap & tilemap generation from a single example with the help of ideas from Quantum Mechanics. GitHub (2016). www.github.com/mxgmn/WaveFunctionCollapse

  5. Karth, I., Smith, A.M.: WaveFunctionCollapse is constraint solving in the wild. In: Proceedings of the 12th International Conference on the Foundations of Digital Games, pp. 1–10, August 2017

    Google Scholar 

  6. Kleineberg, M.: An infinite, procedurally generated city, assembled out of blocks using the Wave Function Collapse algorithm with backtracking. GitHub (2018). www.github.com/marian42/wavefunctioncollapse

  7. Machta, J.: Entropy, information, and computation. Am. J. Phys. 67(12), 1074–1077 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Maji, A.K., Jana, S., Roy, S., Pal, R.K.: An exhaustive study on different sudoku solving techniques. Int. J. Comput. Sci. Issues (IJCSI) 11(2), 247 (2014)

    Google Scholar 

  9. Marín-Lora, C., Chover, M., Sotoca, J.M.: Prototyping a game engine architecture as a multi-agent system. In: 27th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG 2019) (2019)

    Google Scholar 

  10. Marín-Lora, C., Chover, M., Sotoca, J.M., García, L.A.: A game engine to make games as multi-agent systems. Adv. Eng. Softw. 140, 102732 (2020)

    Article  Google Scholar 

  11. Marín-Lora, C., Chover, M., Sotoca, J.M.: A game logic specification proposal for 2D video games. In: Rocha, Á., Adeli, H., Reis, L.P., Costanzo, S., Orovic, I., Moreira, F. (eds.) WorldCIST 2020. AISC, vol. 1159, pp. 494–504. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45688-7_50

    Chapter  Google Scholar 

  12. Marín-Lora, C., Chover, M., Sotoca, J.M.: A multi-agent specification for the Tetris game. In: Matsui, K., Omatu, S., Yigitcanlar, T., González, S.R. (eds.) DCAI 2021. LNNS, vol. 327, pp. 169–178. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-86261-9_17

    Chapter  Google Scholar 

  13. Marín-Lora, C.: Game Development Based on Multi-agent Systems (Doctoral dissertation, Universitat Jaume I) (2022)

    Google Scholar 

  14. Nystrom, R.: Game programming patterns. Genever Benning (2014)

    Google Scholar 

  15. Provan, J.S.: Sudoku: strategy versus structure. Am. Math. Mon. 116(8), 702–707 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rebollo, C., Marín-Lora, C., Remolar, I., Chover, M.: Gamesonomy vs Scratch: two different ways to introduce programming. In: 15th International Conference On Cognition And Exploratory Learning In The Digital Age (CELDA 2018). Ed. IADIS Press (2018)

    Google Scholar 

  17. Russell, E., Jarvis, F.: Mathematics of sudoku II. Math. Spectr. 39(2), 54–58 (2006)

    Google Scholar 

  18. Sbert, M., Feixas, M., Rigau, J., Viola, I., Chover, M.: Applications of information theory to computer graphics. In: Eurographics (Tutorials), pp. 625–704, August 2007

    Google Scholar 

  19. Simonis, H.: Sudoku as a constraint problem. In: CP Workshop on Modeling and Reformulating Constraint Satisfaction Problems, vol. 12, pp. 13–27. Citeseer, October 2005

    Google Scholar 

  20. Stalberg, O.: Townscaper. Steam (2021). www.store.steampowered.com/app/1291340/Townscaper/

  21. Wooldridge, M.: An Introduction to Multiagent Systems. John wiley & sons, Hoboken (2009)

    Google Scholar 

Download references

Acknowledgements

This work has been developed with the support of valgrAI - Graduate School and Research Network of Artificial Intelligence and the Generalitat Valenciana, and co-funded by the European Union. Furthermore, with Grant PDC2021-120997-C31 funded by MCIN/AEI/10.13039/501100011033 by the “European Union NextgenerationEU/PRTR”. Grant to Consolidated Research Groups (CIAICO/2021/037) of the Department of Innovation, Universities, Science and Digital Society (Generalitat Valenciana).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlos Marín-Lora .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Marín-Lora, C., Chover, M. (2023). A Multi-agent Sudoku Through the Wave Function Collapse. In: Malvone, V., Murano, A. (eds) Multi-Agent Systems. EUMAS 2023. Lecture Notes in Computer Science(), vol 14282. Springer, Cham. https://doi.org/10.1007/978-3-031-43264-4_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-43264-4_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43263-7

  • Online ISBN: 978-3-031-43264-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics