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Counting the possible number of shapes.

  1. Nov 17, 2008 #1
    Hello,

    I have an 8 by 8 binary matrix. Define a shape as a cluster of 1's. For instance, consider the following sample:

    Code (Text):


    0 [COLOR="Red"]1[/COLOR] 0 0 0 0 0 0
    0 [COLOR="Red"]1[/COLOR] 0 0 0 0 0 0
    0 0 [COLOR="Red"]1 1[/COLOR] 0 0 0 0
    0 0 0 [COLOR="Red"]1[/COLOR] 0 0 0 [COLOR="Blue"]1[/COLOR]
    0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0
    0 0 0 0 0 [COLOR="DarkOliveGreen"]1 1[/COLOR] 0
    0 0 0 0 0 [COLOR="DarkOliveGreen"]1 1[/COLOR] 0

     
    As you can see, there are three shapes in the above binary matrix. Given the constraint that the matrix cannot have more than 32 ones inside, then how many possible shapes can I get in an 8 by 8 matrix? The shapes which are similar if you rotate them in any direction are considered as one shape...

    Thank you!
     
  2. jcsd
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