Generate a Universal-binary-function Lookup Table

J, 10 (13?) characters

|.|:#:i.16

Number list:

   i.16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15`

to binary:

   #:i.16
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

Transpose:

   |:#:i.16
0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

Reverse:

   |.|:#:i.16
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

Do we need to remove the spaces? Looking at the other J answer it seems we do so we'll need to add 3 characters and borrow the 1": from Jan's answer.

Python 2, 40

for n in 1,2,4,8:print 8/n*('0'*n+'1'*n)

APL (14)

Assuming ⎕IO=0 (that's a setting):

⎕D[⊖(4⍴2)⊤⍳16]

Explanation:

• ⍳16: numbers [0,16)
• (4⍴2)⊤: encode each number in base 2 using 4 digits
• ⊖: horizontal reverse (so the MSB ends up on top)
• ⎕D[...]: select these values from ⎕D which is the string 0123456789. (A numeric matrix is displayed with spaces between the values, a character matrix is not. So this converts each numerical bit to one of the chars '0' '1').