Abelian Sandpile Quilting Blocks
Benjamin R. Trube

Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture
Pages 437–440
Short Papers

Abstract

I use traditional quilting blocks with horizontal and vertical mirror symmetry and/or 4-fold rotational symmetry as boundaries for the Abelian Sandpile Model. I further experiment with using shapes within the quilting blocks to seed different quantities of sand throughout the pile before allowing the sand to topple and stabilize. I observe that the symmetries of the underlying quilting block are maintained, and that the shape of the original seed can be found in the final stabilized pattern.

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