Chip-Firing with Walls and Dying Vertices
Benjamin Trube

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 397–400
Short Papers

Abstract

I experiment with chip-firing models with a non-uniform graph degree, using fixed boundaries to block or redirect the flow of chips within the system. I explore some ways in which these boundaries can be used to affect the stabilized pattern. I then introduce vertex death, which changes the graph degree of the surrounding vertices as their neighbors die, before the chip-firing model has stabilized. I observe that consistent final configurations can be achieved despite these changing dynamics, provided vertex firings and death are handled uniformly.

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