APL Art

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 25

APLers are often teased concerning their use of strange symbols. Curiously enough, even mathematicians are sometimes guilty of this! Whilst teaching students who use APL in their statistics practical I have sometimes caught them playing with the symbols to see just what shapes can be created from them. All good fun though at the time they had better things to do!

Recently I noticed that my wife Claire (who is both a mathematician and an APLer) was doodling with the APL characters, and I began to wonder just how many works of aplart there are out there. So here is Claire’s contribution to start the ball rolling. The program is called LEAR and it defines global variables OWL CAT and BOAT. So there are no prizes for guessing just what LEAR does. As you can see the results are quite good. (I have to say that!) But of course you, the reader can do better?

     ∇ RES←LEAR;O;C;B
[1]    O←' ∧∨⍟π'
[2]    OWL← 6 5 ⍴O[1 2 1 2 1 1 4 3 4 1 ,(15⍴5), 1 5 1 5]
[3]    C←' ∧O=1/_'
[4]    CAT← 7 5 ⍴C[1 2 1 2 1 1 3 1 3 1 1 4 5 4 1 ,(15⍴6), 7 7 7 7 6]
[5]    B←'_ \ / ~'
[6]    BOAT← 3 20 ⍴(20 1 1 16 1 1 20)/B
[7]    RES←((7 ¯8 ↑CAT), 7 12 ↑ ¯7 ¯9 ↑OWL)⍪BOAT
     ∇

    ∧ ∧

    O O      ∧ ∧

    =1=      ⍟∨⍟

   /////    πππππ

   /////    πππππ

   /////    πππππ

   ____/     π π

____________________

 \                /

~~~~~~~~~~~~~~~~~~~~

My contribution to APLART looks forward to the summer and the next international conference APL ’89 to be held in Manhattan, New York. Since I have never been to the Big Apple before I am really excited at the thought of seeing the Empire State Building and other sites. So below is a function, cryptically called ESB, which requires a left argument equal to an integer, and a right argument requiring two positive integers. The result, for suitable choices, is something not dissimilar to part of the Manhattan skyline.

     ∇ R←A ESB N
[1]    R←'⊞ '[1+(⍳N[2])∘.≤A×|(⍳N[1])-⌈N[1]÷2]
     ∇

  3 ESB 11 22

     ⊞

     ⊞

     ⊞

    ⊞⊞⊞

    ⊞⊞⊞

    ⊞⊞⊞

   ⊞⊞⊞⊞⊞

   ⊞⊞⊞⊞⊞

   ⊞⊞⊞⊞⊞

  ⊞⊞⊞⊞⊞⊞⊞

  ⊞⊞⊞⊞⊞⊞⊞

  ⊞⊞⊞⊞⊞⊞⊞

 ⊞⊞⊞⊞⊞⊞⊞⊞⊞

 ⊞⊞⊞⊞⊞⊞⊞⊞⊞

 ⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞⊞

If you are a newcomer to APL, then you may be a bit bemused as to how this function works. The best way to proceed is to assign say N←11 22 and A←3. Then try looking at bits of the code. (Note the use of | which takes the absolute value of its right argument.)

So may I exercise my privilege as editor of Education Vector and offer a prize for the most innovative APLART submission using a maximum of 10 lines of code? Please submit your contributions to the editor at the address at the foot of the front page.