The Shape of Math

1
The Shape of Math

• The Game of Life

Masashi SANAE
2
What is The Game of Life?

• 1970 John Horton Conway Mathematician,
  Cambridge University
• Simulation game
• The symbol of the biological society
• Under the certain enviroment, new life is born.
  Under the depopulation or the state of the
  congestion, the cell perishes.
• Modeling of a living entity in space

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The Rule of The Game of Life

• A grid on the surface
• Put a cell on the space labelled P
• Decide the placement of a new cell according to
  the next rule
• N the number of cells around P
• Survival if N 2 or 3
• Death if N lt 1 or Ngt4
• Birth There isnt a cell on P and N3
• Apply these rules on the all divisions on the
  board at the same time

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Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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0


5
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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0



6
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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? ? ?







0
0
0
0
0
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Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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? ? ?










1




8
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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? ? ?










2



9
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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3


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10
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

1st generation
2nd generation


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2
1
1
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3
3
4
2
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2
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Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

2nd generation
3rd generation

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0 1 2 2 1 1
1 3 4 4 3 1
2 3 4 5 4 3
2 5 6 7 5 3
2 3 4 5 4 3
1 3 4 4 3 1

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12
Example

• Survival If N 2 or 3
• Death If N lt 1 or Ngt4
• Birth There isnt a cell on P and N3

13
Lets Try!
Exercise 1 Exercise 2 Exercise 3



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Lets Try!




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15
Death Type
Patern Of Life
STABILITY TYPE
Repeat type
Another
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STABILITY TYPE
(1) block (2) hive (3) loaf (4) pail

(5) snake (6) boat (7) pond  
 
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repeat TYPE
(1) red light (2) beacon (3) clock

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Another
(1) glider
(2) spaceship