Abelian sandpile model/Identity: Difference between revisions

=={{header|11l}}==

{{trans|Python}}

<lang 11l>T Sandpile

DefaultDict[(Int, Int), Int] grid

F (gridtext)

V array = gridtext.split_py().map(x -> Int(x))

L(x) array

.grid[(L.index I/ 3, L.index % 3)] = x

Set[(Int, Int)] _border = Set(cart_product(-1 .< 4, -1 .< 4).filter((r, c) -> !(r C 0..2) | !(c C 0..2)))

_cell_coords = cart_product(0.<3, 0.<3)

F topple()

V& g = .grid

L(r, c) ._cell_coords

I g[(r, c)] >= 4

g[(r - 1, c)]++

g[(r + 1, c)]++

g[(r, c - 1)]++

g[(r, c + 1)]++

g[(r, c)] -= 4

R 1B

R 0B

F stabilise()

L .topple() {}

L(row_col) ._border.intersection(Set(.grid.keys()))

.grid.pop(row_col)

F ==(other)

R all(._cell_coords.map(row_col -> @.grid[row_col] == @other.grid[row_col]))

F +(other)

V ans = Sandpile(‘’)

L(row_col) ._cell_coords

ans.grid[row_col] = .grid[row_col] + other.grid[row_col]

ans.stabilise()

R ans

F String()

[String] txt

L(row) 3

txt.append((0.<3).map(col -> String(@.grid[(@row, col)])).join(‘ ’))

R txt.join("\n")

V unstable = Sandpile(‘4 3 3

3 1 2

0 2 3’)

V s1 = Sandpile(‘1 2 0

2 1 1

0 1 3’)

V s2 = Sandpile(‘2 1 3

1 0 1

0 1 0’)

V s3 = Sandpile(‘3 3 3 3 3 3 3 3 3’)

V s3_id = Sandpile(‘2 1 2 1 0 1 2 1 2’)

print(unstable)

print()

unstable.stabilise()

print(unstable)

print()

print(s1 + s2)

print()

print(s2 + s1)

print()

print(s1 + s2 == s2 + s1)

print()

print(s3 + s3_id)

print()

print(s3 + s3_id == s3)

print()

print(s3_id + s3_id)

print()

print(s3_id + s3_id == s3_id)</lang>

{{out}}

<pre>

4 3 3

3 1 2

0 2 3

2 1 0

0 3 3

1 2 3

3 3 3

3 1 2

0 2 3

3 3 3

3 1 2

0 2 3

1B

3 3 3

3 3 3

3 3 3

1B

2 1 2

1 0 1

2 1 2

1B

</pre>