Visualize a Difference Pyramid
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IA$ṖÐ¿UṚz”@ṚGḟ”@


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Background

Generating the differences is quite straightforward. For input

[1, 2, 3, 4, 5, 6, 7, 8, 9]


IA$ṖÐ¿ (absolute value of increments while there is more than one element) yields the following ragged 2D array.

[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 0, 0]
[0, 0, 0]
[0, 0]
[0]


U reverses the order of the columns and Ṛ the order of the rows, yielding the following.

[0]
[0, 0]
[0, 0, 0]
[0, 0, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1]
[9, 8, 7, 6, 5, 4, 3, 2, 1]


Now, we transpose rows and columns with z”@, which pads all rows to the same length before transposing. The result is the following.

[0, 0, 0, 0, 0, 0, 0, 1, 9]
[@, 0, 0, 0, 0, 0, 0, 1, 8]
[@, @, 0, 0, 0, 0, 0, 1, 7]
[@, @, @, 0, 0, 0, 0, 1, 6]
[@, @, @, @, 0, 0, 0, 1, 5]
[@, @, @, @, @, 0, 0, 1, 4]
[@, @, @, @, @, @, 0, 1, 3]
[@, @, @, @, @, @, @, 1, 2]
[@, @, @, @, @, @, @, @, 1]


Reversing the rows gives

[@, @, @, @, @, @, @, @, 1]
[@, @, @, @, @, @, @, 1, 2]
[@, @, @, @, @, @, 0, 1, 3]
[@, @, @, @, @, 0, 0, 1, 4]
[@, @, @, @, 0, 0, 0, 1, 5]
[@, @, @, 0, 0, 0, 0, 1, 6]
[@, @, 0, 0, 0, 0, 0, 1, 7]
[@, 0, 0, 0, 0, 0, 0, 1, 8]
[0, 0, 0, 0, 0, 0, 0, 1, 9]


To turn the 2D array into a whitespace-separated string, we use the built-in grid atom (G). It joins columns by spaces and rows by linefeeds, yielding the following result.

@ @ @ @ @ @ @ @ 1
@ @ @ @ @ @ @ 1 2
@ @ @ @ @ @ 0 1 3
@ @ @ @ @ 0 0 1 4
@ @ @ @ 0 0 0 1 5
@ @ @ 0 0 0 0 1 6
@ @ 0 0 0 0 0 1 7
@ 0 0 0 0 0 0 1 8
0 0 0 0 0 0 0 1 9


All that's left to do is removing the padding character with ḟ”@, yielding

        1
       1 2
      0 1 3
     0 0 1 4
    0 0 0 1 5
   0 0 0 0 1 6
  0 0 0 0 0 1 7
 0 0 0 0 0 0 1 8
0 0 0 0 0 0 0 1 9


which is the desired output.