Abelian sandpile model/Identity: Difference between revisions
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* https://en.wikipedia.org/wiki/Abelian_sandpile_model |
* https://en.wikipedia.org/wiki/Abelian_sandpile_model |
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=={{header|Go}}== |
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{{trans|Wren}} |
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<lang go>package main |
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import ( |
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"fmt" |
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"strconv" |
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"strings" |
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) |
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type sandpile struct{ a [9]int } |
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var neighbors = [][]int{ |
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{1, 3}, {0, 2, 4}, {1, 5}, {0, 4, 6}, {1, 3, 5, 7}, {2, 4, 8}, {3, 7}, {4, 6, 8}, {5, 7}, |
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} |
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// 'a' is in row order |
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func newSandpile(a [9]int) *sandpile { return &sandpile{a} } |
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func (s *sandpile) plus(other *sandpile) *sandpile { |
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b := [9]int{} |
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for i := 0; i < 9; i++ { |
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b[i] = s.a[i] + other.a[i] |
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} |
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return &sandpile{b} |
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} |
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func (s *sandpile) isStable() bool { |
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for _, e := range s.a { |
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if e > 3 { |
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return false |
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} |
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} |
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return true |
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} |
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// just topples once so we can observe intermediate results |
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func (s *sandpile) topple() { |
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for i := 0; i < 9; i++ { |
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if s.a[i] > 3 { |
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s.a[i] -= 4 |
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for _, j := range neighbors[i] { |
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s.a[j]++ |
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} |
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return |
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} |
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} |
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} |
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func (s *sandpile) String() string { |
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var sb strings.Builder |
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for i := 0; i < 3; i++ { |
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for j := 0; j < 3; j++ { |
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sb.WriteString(strconv.Itoa(s.a[3*i+j]) + " ") |
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} |
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sb.WriteString("\n") |
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} |
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return sb.String() |
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} |
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func main() { |
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fmt.Println("Avalanche of topplings:\n") |
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s4 := newSandpile([9]int{4, 3, 3, 3, 1, 2, 0, 2, 3}) |
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fmt.Println(s4) |
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for !s4.isStable() { |
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s4.topple() |
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fmt.Println(s4) |
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} |
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fmt.Println("Commutative additions:\n") |
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s1 := newSandpile([9]int{1, 2, 0, 2, 1, 1, 0, 1, 3}) |
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s2 := newSandpile([9]int{2, 1, 3, 1, 0, 1, 0, 1, 0}) |
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s3_a := s1.plus(s2) |
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for !s3_a.isStable() { |
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s3_a.topple() |
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} |
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s3_b := s2.plus(s1) |
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for !s3_b.isStable() { |
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s3_b.topple() |
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} |
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fmt.Printf("%s\nplus\n\n%s\nequals\n\n%s\n", s1, s2, s3_a) |
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fmt.Printf("and\n\n%s\nplus\n\n%s\nalso equals\n\n%s\n", s2, s1, s3_b) |
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fmt.Println("Addition of identity sandpile:\n") |
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s3 := newSandpile([9]int{3, 3, 3, 3, 3, 3, 3, 3, 3}) |
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s3_id := newSandpile([9]int{2, 1, 2, 1, 0, 1, 2, 1, 2}) |
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s4 = s3.plus(s3_id) |
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for !s4.isStable() { |
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s4.topple() |
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} |
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fmt.Printf("%s\nplus\n\n%s\nequals\n\n%s\n", s3, s3_id, s4) |
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fmt.Println("Addition of identities:\n") |
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s5 := s3_id.plus(s3_id) |
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for !s5.isStable() { |
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s5.topple() |
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} |
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fmt.Printf("%s\nplus\n\n%s\nequals\n\n%s", s3_id, s3_id, s5) |
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}</lang> |
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{{out}} |
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<pre> |
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Avalanche of topplings: |
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4 3 3 |
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3 1 2 |
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0 2 3 |
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0 4 3 |
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4 1 2 |
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0 2 3 |
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1 0 4 |
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4 2 2 |
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0 2 3 |
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1 1 0 |
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4 2 3 |
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0 2 3 |
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2 1 0 |
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0 3 3 |
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1 2 3 |
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Commutative additions: |
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1 2 0 |
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2 1 1 |
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0 1 3 |
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plus |
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2 1 3 |
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1 0 1 |
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0 1 0 |
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equals |
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3 3 3 |
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3 1 2 |
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0 2 3 |
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and |
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2 1 3 |
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1 0 1 |
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0 1 0 |
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plus |
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1 2 0 |
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2 1 1 |
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0 1 3 |
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also equals |
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3 3 3 |
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3 1 2 |
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0 2 3 |
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Addition of identity sandpile: |
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3 3 3 |
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3 3 3 |
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3 3 3 |
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plus |
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2 1 2 |
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1 0 1 |
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2 1 2 |
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equals |
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3 3 3 |
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3 3 3 |
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3 3 3 |
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Addition of identities: |
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2 1 2 |
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1 0 1 |
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2 1 2 |
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plus |
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2 1 2 |
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1 0 1 |
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2 1 2 |
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equals |
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2 1 2 |
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1 0 1 |
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2 1 2 |
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</pre> |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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