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To each vertex (''side'', ''field'') <math>(x,y)\in\Gamma</math> of the grid, we associate a value (''grains of sand'', ''slope'', ''particles'') <math>z_0(x,y)\in\{0,1,2,3\}</math>, with <math>z_0\in\{0,1,2,3\}^\Gamma</math> referred to as the (initial) configuration of the sandpile.

To each vertex (''side'', ''field'') <math>(x,y)\in\Gamma</math> of the grid, we associate a value (''grains of sand'', ''slope'', ''particles'') <math>z_0(x,y)\in\{0,1,2,3\}</math>, with <math>z_0\in\{0,1,2,3\}^\Gamma</math> referred to as the (initial) configuration of the sandpile.

对于网格的每个顶点（“边”、“场”）<math>（x，y），\Gamma</math>中，我们将0,1,2,3\}</math>中的值（“沙粒”、“坡度”、“粒子”）zu0（x，y）与称为沙堆（初始）配置的<math>z\u联系在一起。

对于网格的每个顶点（“边”、“场”）<math>(x,y)\in\Gamma</math>中，我们将{0,1,2,3\}</math>中的值（“沙粒”、“坡度”、“粒子”）<math>z_0(x,y)\in\{0,1,2,3\}</math>与称为沙堆（初始）配置的<math>z_0\in\{0,1,2,3\}^\Gamma</math>联系在一起。

The definition of the sandpile model given above for finite rectangular grids \Gamma\subset\mathbb{Z}^2 of the standard square lattice \mathbb{Z}^2 can then be seen as a special case of this definition: consider the graph G=(V,E) which is obtained from \Gamma by adding an additional vertex, the sink, and by drawing additional edges from the sink to every boundary vertex of \Gamma such that the degree of every non-sink vertex of G is four. In this manner, also sandpile models on non-rectangular grids of the standard square lattice (or of any other lattice) can be defined: Intersect some bounded subset S of \mathbb{R}^2 with \mathbb{Z}^2. Contract every edge of \mathbb{Z}^2 whose two endpoints are not in S\cap\mathbb{Z}^2. The single remaining vertex outside of S\cap\mathbb{Z}^2 then constitutes the sink of the resulting sandpile graph.

The definition of the sandpile model given above for finite rectangular grids \Gamma\subset\mathbb{Z}^2 of the standard square lattice \mathbb{Z}^2 can then be seen as a special case of this definition: consider the graph G=(V,E) which is obtained from \Gamma by adding an additional vertex, the sink, and by drawing additional edges from the sink to every boundary vertex of \Gamma such that the degree of every non-sink vertex of G is four. In this manner, also sandpile models on non-rectangular grids of the standard square lattice (or of any other lattice) can be defined: Intersect some bounded subset S of \mathbb{R}^2 with \mathbb{Z}^2. Contract every edge of \mathbb{Z}^2 whose two endpoints are not in S\cap\mathbb{Z}^2. The single remaining vertex outside of S\cap\mathbb{Z}^2 then constitutes the sink of the resulting sandpile graph.