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edited Jun 9, 2012 at 14:53

31.2k
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APL (5251)

      A←67⍴0⋄A[34]←1⋄' ○'[1+32 67⍴{~⊃⍵:⍵,∇~∇(1⌽⍵)=¯1⌽⍵⋄⍬≠¯1⌽⍵⋄⍬}A]

A←67⍴0: A is a vector of 67 zeroes
A[34]←1: the 34th element is 1
{...}A: starting with A, do:
~⊃⍵:: if the first element of the current row is zero
⍵,∇: add the current row to the answer, and recurse with:
~(1⌽⍵)=¯1⌽⍵≠¯1⌽⍵: the vector where each element is the XOR of its neighbours in the previous generation
⋄⍬: otherwise, we're done
32 67⍴: format this in a 67x32 matrix
1+: add one to select the right value from the character array
' ○'[...]: output either a space (not part of the triangle) or a circle (when it is part of the triangle)

APL (52)

      A←67⍴0⋄A[34]←1⋄' ○'[1+32 67⍴{~⊃⍵:⍵,∇~(1⌽⍵)=¯1⌽⍵⋄⍬}A]

A←67⍴0: A is a vector of 67 zeroes
A[34]←1: the 34th element is 1
{...}A: starting with A, do:
~⊃⍵:: if the first element of the current row is zero
⍵,∇: add the current row to the answer, and recurse with:
~(1⌽⍵)=¯1⌽⍵: the vector where each element is the XOR of its neighbours in the previous generation
⋄⍬: otherwise, we're done
32 67⍴: format this in a 67x32 matrix
1+: add one to select the right value from the character array
' ○'[...]: output either a space (not part of the triangle) or a circle (when it is part of the triangle)

APL (51)

      A←67⍴0⋄A[34]←1⋄' ○'[1+32 67⍴{~⊃⍵:⍵,∇(1⌽⍵)≠¯1⌽⍵⋄⍬}A]

A←67⍴0: A is a vector of 67 zeroes
A[34]←1: the 34th element is 1
{...}A: starting with A, do:
~⊃⍵:: if the first element of the current row is zero
⍵,∇: add the current row to the answer, and recurse with:
(1⌽⍵)≠¯1⌽⍵: the vector where each element is the XOR of its neighbours in the previous generation
⋄⍬: otherwise, we're done
32 67⍴: format this in a 67x32 matrix
1+: add one to select the right value from the character array
' ○'[...]: output either a space (not part of the triangle) or a circle (when it is part of the triangle)

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created Jun 9, 2012 at 13:30

marinus

31.2k
7
71
112

APL (52)

      A←67⍴0⋄A[34]←1⋄' ○'[1+32 67⍴{~⊃⍵:⍵,∇~(1⌽⍵)=¯1⌽⍵⋄⍬}A]

Explanation:

A←67⍴0: A is a vector of 67 zeroes
A[34]←1: the 34th element is 1
{...}A: starting with A, do:
~⊃⍵:: if the first element of the current row is zero
⍵,∇: add the current row to the answer, and recurse with:
~(1⌽⍵)=¯1⌽⍵: the vector where each element is the XOR of its neighbours in the previous generation
⋄⍬: otherwise, we're done
32 67⍴: format this in a 67x32 matrix
1+: add one to select the right value from the character array
' ○'[...]: output either a space (not part of the triangle) or a circle (when it is part of the triangle)

Output:

                                 ○                                 
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                          ○ ○ ○ ○ ○ ○ ○ ○                          
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                 ○                               ○                 
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               ○   ○                           ○   ○               
              ○ ○ ○ ○                         ○ ○ ○ ○              
             ○       ○                       ○       ○             
            ○ ○     ○ ○                     ○ ○     ○ ○            
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          ○ ○ ○ ○ ○ ○ ○ ○                 ○ ○ ○ ○ ○ ○ ○ ○          
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     ○       ○       ○       ○       ○       ○       ○       ○     
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