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Comment by jesuslop | Hacker News Reader

You get those also doing a Pascal triangle mod 2, so a xor. Is a zoom-out fractal as oposed to Mandelbrot set.

True. pas.f in Forth

    : .r u.r ;
    : position  ( row -- )  cr  33 swap 2 *  - spaces  ;
    : pas ( 0 ... 0 -- 0 ... 0 )    0 >r begin
    over + >r  dup 0= until
    begin  r> dup while  dup 4 .r  repeat  ;
    : pass  ( -- )    0 1 0    18 0 ?do  dup position  >r  pas  r>  1+  loop      drop  ;
    : pax  ( 0 ... 0 -- )  drop begin 0= until ;
    : pascal  ( -- )  pass pax ;

    pascal
    cr

The same mod2:

    : .r u.r ;
    : position  ( row -- )  cr  33 swap 2 *  - spaces  ;
    : pas ( 0 ... 0 -- 0 ... 0 )    0 >r begin
     over + >r  dup 0= until
     begin  r> dup while  dup 2 mod 4 .r  repeat  ;
    : pass  ( -- )    0 1 0    18 0 ?do  dup position  >r  pas  r>  1+  loop     drop  ;
    : pax  ( 0 ... 0 -- )  drop begin 0= until ;
    : pascal  ( -- )  pass pax ;

    pascal
    cr

A Forth for people in a hurry:

     git clone https://github.com/howerj/subleq
     cd subleq
     sed -i 's,0 constant opt.control,1 constant opt.control,g' subleq.fth
     gmake subleq
     ./subleq subleq.dec < subleq.fth > new.dec
     ./subleq new.dec < pas.f

Output from `cr pascal` in GForth:

                                    1
                                  1   1
                                1   0   1
                              1   1   1   1
                            1   0   0   0   1
                          1   1   0   0   1   1
                        1   0   1   0   1   0   1
                      1   1   1   1   1   1   1   1
                    1   0   0   0   0   0   0   0   1
                  1   1   0   0   0   0   0   0   1   1
                1   0   1   0   0   0   0   0   1   0   1
              1   1   1   1   0   0   0   0   1   1   1   1
            1   0   0   0   1   0   0   0   1   0   0   0   1
          1   1   0   0   1   1   0   0   1   1   0   0   1   1
        1   0   1   0   1   0   1   0   1   0   1   0   1   0   1
      1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
    1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1 ok

By changing `4 .r` to `bl + dup dup dup emit emit emit emit` I get this:

                                      !!!!
                                    !!!!!!!!
                                  !!!!    !!!!
                                !!!!!!!!!!!!!!!!
                              !!!!            !!!!
                            !!!!!!!!        !!!!!!!!
                          !!!!    !!!!    !!!!    !!!!
                        !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                      !!!!                            !!!!
                    !!!!!!!!                        !!!!!!!!
                  !!!!    !!!!                    !!!!    !!!!
                !!!!!!!!!!!!!!!!                !!!!!!!!!!!!!!!!
              !!!!            !!!!            !!!!            !!!!
            !!!!!!!!        !!!!!!!!        !!!!!!!!        !!!!!!!!
          !!!!    !!!!    !!!!    !!!!    !!!!    !!!!    !!!!    !!!!
        !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
      !!!!                                                            !!!!
    !!!!!!!!                                                        !!!!!!!! ok

But this is not using bitwise AND, just the Pascal's triangle approach. (Interestingly, you can reformulate that as a neighborhood-2 2-state 1-dimensional cellular automaton pretty easily; it occurs in a couple of different guises in Wolfram's catalog.)

Here's an ASCII-art version that uses AND as Michał describes:

    32 value size  : line cr size 0 do dup i and if bl else [char] # then dup emit emit loop drop ;
    : pasand size 0 do i line loop ;

Running `pasand` then yields this:

    ################################################################
    ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  ##  
    ####    ####    ####    ####    ####    ####    ####    ####    
    ##      ##      ##      ##      ##      ##      ##      ##      
    ########        ########        ########        ########        
    ##  ##          ##  ##          ##  ##          ##  ##          
    ####            ####            ####            ####            
    ##              ##              ##              ##              
    ################                ################                
    ##  ##  ##  ##                  ##  ##  ##  ##                  
    ####    ####                    ####    ####                    
    ##      ##                      ##      ##                      
    ########                        ########                        
    ##  ##                          ##  ##                          
    ####                            ####                            
    ##                              ##                              
    ################################                                
    ##  ##  ##  ##  ##  ##  ##  ##                                  
    ####    ####    ####    ####                                    
    ##      ##      ##      ##                                      
    ########        ########                                        
    ##  ##          ##  ##                                          
    ####            ####                                            
    ##              ##                                              
    ################                                                
    ##  ##  ##  ##                                                  
    ####    ####                                                    
    ##      ##                                                      
    ########                                                        
    ##  ##                                                          
    ####                                                            
    ##                                                               ok

Straight from the blog, too, from C to Forth:

   : sier cr 32 0 do 32 0 do i j and if ."   " else ." * " then loop cr loop ;
   sier

Output from eforth/subleq (with do...loop set in the config):

    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
    *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   
    * *     * *     * *     * *     * *     * *     * *     * *     
    *       *       *       *       *       *       *       *       
    * * * *         * * * *         * * * *         * * * *         
    *   *           *   *           *   *           *   *           
    * *             * *             * *             * *             
    *               *               *               *               
    * * * * * * * *                 * * * * * * * *                 
    *   *   *   *                   *   *   *   *                   
    * *     * *                     * *     * *                     
    *       *                       *       *                       
    * * * *                         * * * *                         
    *   *                           *   *                           
    * *                             * *                             
    *                               *                               
    * * * * * * * * * * * * * * * *                                 
    *   *   *   *   *   *   *   *                                   
    * *     * *     * *     * *                                     
    *       *       *       *                                       
    * * * *         * * * *                                         
    *   *           *   *                                           
    * *             * *                                             
    *               *                                               
    * * * * * * * *                                                 
    *   *   *   *                                                   
    * *     * *                                                     
    *       *                                                       
    * * * *                                                         
    *   *                                                           
    * *                                                             
    *                                                               
     ok
     ok

That looks nicer than my version. But you should put the `cr` before the inner loop, not after it. That way you can remove the `cr` before the outer loop.

Nothing much to do with your great post, but I almost REALLY liked that first pyramid, but the last line being off threw me visually, so I had to straighten it out:

                                    1
                                  1   1
                                1   0   1
                              1   1   1   1
                            1   0   0   0   1
                          1   1   0   0   1   1
                        1   0   1   0   1   0   1
                      1   1   1   1   1   1   1   1
                    1   0   0   0   0   0   0   0   1
                  1   1   0   0   0   0   0   0   1   1
                1   0   1   0   0   0   0   0   1   0   1
              1   1   1   1   0   0   0   0   1   1   1   1
            1   0   0   0   1   0   0   0   1   0   0   0   1
          1   1   0   0   1   1   0   0   1   1   0   0   1   1
        1   0   1   0   1   0   1   0   1   0   1   0   1   0   1
      1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
    1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
  1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1

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