Square Numbers

Look at these patterns made from tiles:

  black tile   black tilewhite tile
white tileblack tile
 
  black tilewhite tileblack tile
white tileblack tilewhite tile
black tilewhite tileblack tile
 
  black tilewhite tileblack tilewhite tile
white tileblack tilewhite tileblack tile
black tilewhite tileblack tilewhite tile
white tileblack tilewhite tileblack tile
 
Pattern 1 Pattern 2 Pattern 3 Pattern 4
                 

 What do you notice?
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