Still Life

A look into a category of life-forms, namely the still life.

What are still life?

Still life are one of the most common forms of life. All life forms, after a certain number of ticks, will become stable. There are three types of stable patterns. The first are the oscillators, the second are the spaceships and last but not least are the still lifes. Still lifes are such that they do not lose or gain any cells during a tick. In other words, they never change their form or position no matter how many ticks have passed. A few examples of still life are shown below:

Still Life of 4 cells

00
00

A block.

 0 
0 0
 0

A tub.

Still Life of 5 cells

 0 
0 0
 00

A boat.

Still Life of 6 cells

 00 
0  0
 00

A beehive.

0 00
00 0

A snake.

A barge.

00 
0 0
 00

A ship.

00  
0  0
  00

An aircraft carrier.

Still Life of 7 cells

A loaf.

A long boat.

00   
0 0 0
   00

A long snake.

A fishhook.

Still Life of 8 cells

A pond.

A long barge.

A long ship.

A shillelagh.

A sinking ship.

Other Still Life

A hat.

A honeycomb.

A lake.

And here's another common configuration:

     0     
    0 0    
    0 0    
     0     
 00     00 
0  0   0  0
 00     00 
     0     
    0 0    
    0 0    
     0

A honey farm.

Hope that list wasn't too long and boring. In each of those patterns, no cell had less than 2 or more than 3 neighbours, and no empty cell has exactly 3 neighbours. Now for some hopefully interesting facts:

There are no still life with exactly 3 cells(can you see why?).

There are only 2 still lifes with exactly 4 cells.

There is only 1 still life with exactly 5 cells.

There are 5 still lifes with exactly 6 cells.

There are 4 still lifes with exactly 7 cells.

There are 9 still lifes with exactly 8 cells.

There are 10 still lifes with exactly 9 cells.

There are 25 still lifes with exactly 10 cells.

There are 46 still lifes with exactly 11 cells.

There are 121 still lifes with exactly 12 cells.

There are 149 still lifes with exactly 13 cells.

I did say hopefully. With an increasing number of cells the number of still lifes increase very rapidly. To end off this section, feast your eyes on this monstrousity of a still life:

          00  00                      
         0 0  0 0                     
        0   00   0                    
       0          0                   
      0            0                  
     0              0                 
    0                0                
   0                  0               
  0                    0              
 0                      0             
0                        0            
00                      00            
  0                    0  00          
  0                    0  0 0         
00                      00   0        
0                             0       
 0                             0      
  0                             0     
   0                             0    
    0                             0   
     0                             0  
      0                             0 
       0   00                        0
        0 0  0                      00
         00  0                     0  
           00                      0  
           0                        00
            0                        0
             0                      0 
              0                    0  
               0                  0   
                0                0    
                 0              0     
                  0            0      
                   0          0       
                    0   00   0        
                     0 0  0 0         
                      00  00

A pool table. It's actually stable.

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