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  • x &= 0b01010101; // mask out just the bits we want ( 0A0B0C0D )
    x *= 0b0011; // this makes ( AABBCCDD )
    x &= 0b01100110; // mask out again ( 0AB00CD0 )
    x *= 0b0101; // this makes ( ABABCDCD0 )
    x &= 0b01111000; // mask out again ( 0ABCD000 )
    x >>= 3; // shift back ( 0000ABCD )
    // to...
    ((((x&0b01010101)*0b0011)&0b01100110)*0b­0101&0b01111000)>>3
    // and pushed through a minifier...
    (5*(3*(x&85)&102)&120)>>3
    

    and then it all got a bit ridiculous:

    g = Graphics.createArrayBuffer(8,8,2);
    g.setColor(1);
    g.drawLine(0,0,7,7);
    g.setColor(2);
    g.drawLine(7,0,0,7);
    
    
    a = g.buffer;
    
    // minified...
    // ((((x&0b01010101)*0b0011)&0b01100110)*0b­0101&0b01111000)>>3  -> 5*(3*(a[0]&85)&102)&120)>>3
    // ((((x&0b10101010)*0b0011)&0b11001100)*0b­0101&0b11110000)>>4  -> 5*(3*(a[0]&170)&204)&240)>>4 
    
    b = new Uint8Array([ 
    (5*(3*(a[0]&85)&102)&120)>>3 | (5*(3*(a[1]&85)&102)&120)<<1, (5*(3*(a[0]&170)&204)&240)>>4 | (5*(3*(a[1]&170)&204)&240), 
    (5*(3*(a[2]&85)&102)&120)>>3 | (5*(3*(a[3]&85)&102)&120)<<1, (5*(3*(a[2]&170)&204)&240)>>4 | (5*(3*(a[3]&170)&204)&240), 
    (5*(3*(a[4]&85)&102)&120)>>3 | (5*(3*(a[5]&85)&102)&120)<<1, (5*(3*(a[4]&170)&204)&240)>>4 | (5*(3*(a[5]&170)&204)&240), 
    (5*(3*(a[6]&85)&102)&120)>>3 | (5*(3*(a[7]&85)&102)&120)<<1, (5*(3*(a[6]&170)&204)&240)>>4 | (5*(3*(a[7]&170)&204)&240), 
    (5*(3*(a[8]&85)&102)&120)>>3 | (5*(3*(a[9]&85)&102)&120)<<1, (5*(3*(a[8]&170)&204)&240)>>4 | (5*(3*(a[9]&170)&204)&240), 
    (5*(3*(a[10]&85)&102)&120)>>3 | (5*(3*(a[11]&85)&102)&120)<<1, (5*(3*(a[10]&170)&204)&240)>>4 | (5*(3*(a[11]&170)&204)&240), 
    (5*(3*(a[12]&85)&102)&120)>>3 | (5*(3*(a[13]&85)&102)&120)<<1, (5*(3*(a[12]&170)&204)&240)>>4 | (5*(3*(a[13]&170)&204)&240), 
    (5*(3*(a[14]&85)&102)&120)>>3 | (5*(3*(a[15]&85)&102)&120)<<1, (5*(3*(a[14]&170)&204)&240)>>4 | (5*(3*(a[15]&170)&204)&240)
    ]);
     
    
    c = new Uint16Array(b.buffer);
    for (i in c) print((c[i]|0x10000).toString(2).substr(­1));
    
    // outputs
    1000000000000001
    0100000000000010
    0010000000000100
    0001000000001000
    0000100000010000
    0000010000100000
    0000001001000000
    0000000110000000
    

    And to swap the quadrants around, all you've got to do is swap the a[0,2,4,6] with a[9,11,13,15] in the insane block of code above.

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