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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Danbaba, A.: Construction and analysis of samurai sudoku. Int. J. Math. Comput. Sci. 10(4), 165–170 (2016)
Felgenhauer, B., Jarvis, F.: Mathematics of sudoku I. Math. Spectr. 39(1), 15–22 (2006)
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
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
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
Machta, J.: Entropy, information, and computation. Am. J. Phys. 67(12), 1074–1077 (1999)
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)
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)
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)
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
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
Marín-Lora, C.: Game Development Based on Multi-agent Systems (Doctoral dissertation, Universitat Jaume I) (2022)
Nystrom, R.: Game programming patterns. Genever Benning (2014)
Provan, J.S.: Sudoku: strategy versus structure. Am. Math. Mon. 116(8), 702–707 (2009)
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)
Russell, E., Jarvis, F.: Mathematics of sudoku II. Math. Spectr. 39(2), 54–58 (2006)
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
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
Stalberg, O.: Townscaper. Steam (2021). www.store.steampowered.com/app/1291340/Townscaper/
Wooldridge, M.: An Introduction to Multiagent Systems. John wiley & sons, Hoboken (2009)
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
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)