Our sandpiles are based on a 3 by 3 rectangular grid giving nine areas that 
contain a number from 0 to 3 inclusive. (The numbers are said to represent 
grains of sand in each area of the sandpile).

E.g. <code>s1</code> =
<pre>    
    1 2 0
    2 1 1
    0 1 3
</pre>

and <code>s2</code> =
<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>
              1 2 0     2 1 3     3 3 3
    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 
those areas cause the whole sandpile to become "unstable" and the sandpile 
areas are "toppled" in an "avalanche" until the "stable" result is obtained.

Any unstable area (with a number >= 4), is "toppled" by loosing one grain of 
sand to each of its four horizontal or vertical neighbours. Grains are lost 
at the edge of the grid, but otherwise increase the number in neighbouring 
cells by one, whilst decreasing the count in the toppled cell by four in each 
toppling.

A toppling may give an adjacent area more than four grains of sand leading to
a chain of topplings called an "avalanche".
E.g.
<pre>    
    4 3 3     0 4 3     1 0 4     1 1 0     2 1 0
    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. 

'''Note:''' The order in which cells are toppled does not affect the final result.

;Task:
* Create a class or datastructure and functions to represent and operate on sandpiles. 
* Confirm the result of the avalanche of topplings shown above
* 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 examples.


;References:
*    https://www.youtube.com/watch?v=1MtEUErz7Gg
*    https://en.wikipedia.org/wiki/Abelian_sandpile_model
<br><br>

