21 citations · 60 across the 4 of their papers we have counts for
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Deterministic Abelian Sandpile and square-triangle tilings
Sergio Caracciolo, Guglielmo Paoletti, Andrea Sportiello
The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. I…
Multiple and inverse topplings in the Abelian Sandpile Model
Sergio Caracciolo, Guglielmo Paoletti, Andrea Sportiello
The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resembling avalanches in piles of sand. The fundamental moves…
Conservation laws for strings in the Abelian Sandpile Model
Sergio Caracciolo, Guglielmo Paoletti, Andrea Sportiello
The Abelian Sandpile generates complex and beautiful patterns and seems to display allometry. On the plane, beyond patches, patterns periodic in both dimensions, we remark the pres…
Explicit characterization of the identity configuration in an Abelian Sandpile Model
Sergio Caracciolo, Guglielmo Paoletti, Andrea Sportiello
Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi…