How to resolve the algorithm Abelian sandpile model step by step in the Lua programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Abelian sandpile model step by step in the Lua programming language

Table of Contents

Problem Statement

Implement the Abelian sandpile model also known as Bak–Tang–Wiesenfeld model. Its history, mathematical definition and properties can be found under its wikipedia article. The task requires the creation of a 2D grid of arbitrary size on which "piles of sand" can be placed. Any "pile" that has 4 or more sand particles on it collapses, resulting in four particles being subtracted from the pile and distributed among its neighbors. It is recommended to display the output in some kind of image format, as terminal emulators are usually too small to display images larger than a few dozen characters tall. As an example of how to accomplish this, see the Bitmap/Write a PPM file task. Examples up to 2^30, wow! javascript running on web Examples:

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Step by Step solution about How to resolve the algorithm Abelian sandpile model step by step in the Lua programming language

Source code in the lua programming language

local sandpile = {
  init = function(self, dim, val)
    self.cell, self.dim = {}, dim
    for r = 1, dim do
      self.cell[r] = {}
      for c = 1, dim do
        self.cell[r][c] = 0
      end
    end
    self.cell[math.floor(dim/2)+1][math.floor(dim/2)+1] = val
  end,
  iter = function(self)
    local dim, cel, more = self.dim, self.cell
    repeat
      more = false
      for r = 1, dim do
        for c = 1, dim do
          if cel[r][c] >= 4 then
            cel[r][c] = cel[r][c] - 4
            if c > 1 then cel[r][c-1], more = cel[r][c-1]+1, more or cel[r][c-1]>=3 end
            if c < dim then cel[r][c+1], more = cel[r][c+1]+1, more or cel[r][c+1]>=3 end
            if r > 1 then cel[r-1][c], more = cel[r-1][c]+1, more or cel[r-1][c]>=3 end
            if r < dim then cel[r+1][c], more = cel[r+1][c]+1, more or cel[r+1][c]>=3 end
          end
          more = more or cel[r][c] >= 4
        end
      end
    until not more
  end,
  draw = function(self)
    for r = 1, self.dim do
      print(table.concat(self.cell[r]," "))
    end
  end,
}
sandpile:init(15, 256)
sandpile:iter()
sandpile:draw()


  

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