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Abelian sandpile model/Identity: Difference between revisions
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added whitespace, changed an Or to an And, pluralized "example".
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E.g. <code>s1</code> =
<pre>
1 2 0
2 1 1
0 1 3
</pre>
<pre>
2 1 3
1 0 1
0 1 0
</pre>
Addition on sandpiles is done by adding numbers in corresponding grid areas,
so for the above:
<pre>
s1 + s2 = 2 1 1 + 1 0 1 = 3 1 2
0 1 3 0 1 0 0 2 3
</pre>
If the addition would result in more than 3 "grains of sand" in any area then
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a chain of topplings called an "avalanche".
E.g.
<pre>
3 1 2 ==> 4 1 2 ==> 4 2 2 ==> 4 2 3 ==> 0 3 3
0 2 3 0 2 3 0 2 3 0 2 3 1 2 3
</pre>
The final result is the stable sandpile on the right.
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* Confirm that s1 + s2 == s2 + s1 # Show the stable results
* If s3 is the sandpile with number 3 in every grid area, and s3_id is the following sandpile:
<pre>
2 1 2
1 0 1
2 1 2
</pre>
: * Show that <code>s3 + s3_id == s3</code>▼
: * Show that <code>s3_id + s3_id == s3_id</code>▼
▲Show confirming output here, with your example.
;References:
* https://www.youtube.com/watch?v=1MtEUErz7Gg
* https://en.wikipedia.org/wiki/Abelian_sandpile_model
<br><br>
=={{header|AArch64 Assembly}}==
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