Chip-Firing Revisited
A Peek into the Third Dimension
Martin Skrodzki (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Ulrich Reitebuch (Freie Universität Berlin)
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Abstract
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.