Comment by Pompidou

the top comment trick [ n, 1, n + 1, 0 ][n % 4] can be implemented in J as following :

   f =: ]`1:`>:`0:@.(4&|)"0

Then:

   (,. ; #: ; [: #: f) i.16

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

....