the shape of math r09 vol.3 the life game ０９．０８．０ ４ masashi sanae
DESCRIPTION
The Rule of The Life Game 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 =4 Birth ： There isn’t a cell on “P” and N=3 Apply these rules on the all divisions on the board at the same timeTRANSCRIPT
The Shape of Math R09
VOL.3 The Life Game
０９．０８．０４Masashi SANAE
What is The Life Game ?
1970 John Horton Conway Mathematician, Cambridge University
Simulation gameThe symbol of the biological societyUnder 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
The Rule of The Life GameA 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 <= 1 or N>=4
Birth ： There isn’t a cell on “P” and N=3
Apply these rules on the all divisions on the board
at the same time
Example
×
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1st generation 2nd generation
×
××
0
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
● ● ●
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1st generation 2nd generation
× ×
×
0
××
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
● ● ●
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1st generation 2nd generation
0 0 0 0
0
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
● ● ●
● ● ●
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1st generation 2nd generation
× × ×
1×
××
×
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
● ● ●
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1st generation 2nd generation
× × ×
2×
×
×
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
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1st generation 2nd generation
× × ×
3×× ●
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
Example
×
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1st generation 2nd generation
2 1
1
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●3 ●3
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
4 2● 2
31 5 8 4 3
31 3 4 2 2
10 2 3 2 1
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Example
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2nd generation
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
3rd generation
Survival ： If N = 2 or 3Death ： If N <= 1 or N>=4Birth ： There isn’t a cell on “P” and N=3
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Let’s Try!
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Exercise 1
Exercise 2
Answer 1
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1st generation
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2nd generation
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3rd generation
Answer 2
1st generation2nd generation3rd generation
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4th generation
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(1) block (2) hive (3) loaf (4) pail
(5) snake (6) boat (7) pond
(1) red light (2) beacon (3) clock
(1) glider
(2) spaceship