scholarly journals DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950032
Author(s):  
WILFRIED HUSS ◽  
ECATERINA SAVA-HUSS
Keyword(s):  
Growth Model ◽  
Sierpinski Gasket ◽  
Internal Diffusion ◽  
Exact Representation ◽  
Sierpiński Gasket ◽  
Diffusion Limited Aggregation ◽  
Sandpile Model ◽  
Diffusion Limited ◽  
Graph Metric ◽  
Divisible Sandpile

The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres [Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal. 30(1) (2009) 1–27] as a tool to study internal diffusion limited aggregation. In this work, we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket [Formula: see text]. We show that the shape is a ball in the graph metric of [Formula: see text]. Moreover, we give an exact representation of the odometer function of the divisible sandpile.

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

scholarly journals Sandpile model on the Sierpinski gasket fractal

1996 ◽  
Vol 54 (1) ◽  
pp. 272-277 ◽  
Author(s):  
Brigita Kutnjak-Urbanc ◽  
Stefano Zapperi ◽  
Sava Milošević ◽  
H. Eugene Stanley
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Sandpile Model

scholarly journals Internal Diffusion Limited Aggregation

1992 ◽  
Vol 20 (4) ◽  
pp. 2117-2140 ◽  
Author(s):  
Gregory F. Lawler ◽  
Maury Bramson ◽  
David Griffeath
Keyword(s):  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited
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