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In Proceedings of Proceedings of Bridges 2022: Mathematics, Music, Art, Architecture, Education, Culture.

Chip-Firing Revisited: A Peek into the Third Dimension

Martin Skrodzki and Ulrich Reitebuch

Running chip-firing on a cubical grid with six neighbors on various uniform backgrounds.

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Chip-firing was first introduced as a probabilistic game. Subsequently, it was generalized to arbitrary graph configurations and investigated mostly with regard to two-dimensional quad-grid layouts. In this paper, we lift chip-firing to the third dimension. Aside from the arising three-dimensional shapes, we are interested in the internal, two-dimensional structures. Furthermore, we explore the different shapes obtained by chip firing processes on various neighborhoods, such as the face-centered and the cube-centered grid as well as on a neighborhood inspired by knight moves.

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Martin Skrodzki and Ulrich Reitebuch, Chip-Firing Revisited: A Peek into the Third Dimension, In Proceedings of Proceedings of Bridges 2022: Mathematics, Music, Art, Architecture, Education, Culture., pp. 221–228, 2022.

BibTex 

@inproceedings{bib:skrodzki:2022,
    author       = { Skrodzki, Martin and Reitebuch, Ulrich },    
    title        = { Chip-Firing Revisited: A Peek into the Third Dimension },
    booktitle    = { In Proceedings of Proceedings of Bridges 2022: Mathematics, Music, Art, Architecture, Education, Culture. },
    year         = { 2022 },
    pages        = { 221--228 },
    url          = { https://publications.graphics.tudelft.nl/papers/32 },
}