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

●

●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