Chip-Firing Revisited: A Peek into the Third Dimension

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.

@InProceedings { SR22,
  author       = "Skrodzki, Martin and Reitebuch, Ulrich",
  title        = "Chip-Firing Revisited: A Peek into the Third Dimension",
  booktitle    = "Proceedings of Bridges 2022: Mathematics, Music, Art, Architecture, Education, Culture.",
  pages        = "221--228",
  year         = "2022",
  url          = "http://graphics.tudelft.nl/Publications-new/2022/SR22"
}