How to resolve the algorithm Abelian sandpile model step by step in the XPL0 programming language

Published on 12 May 2024 09:40 PM
#Xpl0

How to resolve the algorithm Abelian sandpile model step by step in the XPL0 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 XPL0 programming language

Source code in the xpl0 programming language

def  Size = 200;
char Pile1(Size*Size), Pile2(Size*Size);
int  Spigot, I, X, Y;
[SetVid($13);   \VGA 320x200x8
FillMem(Pile1, 0, Size*Size);
FillMem(Pile2, 0, Size*Size);
Spigot:= 400_000;
repeat  I:= 0;
        for Y:= 0 to Size-1 do
            for X:= 0 to Size-1 do
                [if X=Size/2 & Y=Size/2 then
                    [Spigot:= Spigot-4;
                     Pile1(I):= Pile1(I)+4;
                    ];
                if Pile1(I) >= 4 then
                    [Pile1(I):= Pile1(I)-4;
                     Pile2(I-1):= Pile2(I-1)+1;
                     Pile2(I+1):= Pile2(I+1)+1;
                     Pile2(I-Size):= Pile2(I-Size)+1;
                     Pile2(I+Size):= Pile2(I+Size)+1;
                    ];
                Point(X, Y, Pile1(I)*2);
                I:= I+1;
                ];
        I:= Pile1;  Pile1:= Pile2;  Pile2:= I;
until   Spigot < 4;
]

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