The Shape of Math

The Life Game

Masashi 　SANAE

What is The Life Game ?

1970 John Horton Conway

Mathematician, Cambridge UniversitySimulation 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 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 <= 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

Survival ：

If N = 2 or 3

Death ：

If N <= 1 or N>=4

Birth ：

There isn’t a cell on “P” and

N=3

Example

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

×

● ● ●

● ● ●

● ● ●

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

●

●

●

●●

●

Example

●

● ● ●

● ●

● ● ●

●

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

● ●

● ● ● ●

● ● ●

● ● ● ●

● ●

Let’s Try!Exercise 1 Exercise 2 Exercise 3

　 　 　 　 　 　

　 ● ● 　 　 　

　 ● ● ● 　 　

　 　 ● 　 　 　

　 　 　 　 　 　

　 　 　 　 　 　

　 　 　 　 　 　

　 　 　 　 　 　

　 　 　 ● 　 　

　 ● ● ● 　 　

　 　 ● 　 ● 　

　 　 　 　 　 　

　 　 　 　 　 　

　 　 　 　 　 　

　 　 ● 　 　 　

　 ● ● ● 　 　

　 　 　 　 　 　

　 　 　 　 　 　

DEMO DEMO DEMO

1 11 1 1

1

1 11

1 1 1

11 1 1

1 11

1 11 11 1

1 1

1 11 11 1

1 1

1 11 11 1

1 1

1 11 11 1

1 1

1 11 11 1

1 1

STABILITY TYPE

1

1 1 1

1 1

1

1 1

1 1

1 1

1 1

1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

STABILITY TYPE

11 1 1

1 1 11 1 11

11 1

1 1 1

11

1 111

1 1 11 11 1 1

11 1

1 11 11

11 1 1

1 1 1 11 1 11

1 1 11 11 11 11 1 1

11 1 1

1 1 11 1 1 1 1 11 1 11 1 11

1 1 1

1 11 11 1

1 1 1

111

1 1 1 1 1 1

111

1 1 1

1 11 11 1

1 1 1

REPEAT TYPE

PaternOf

Life

DEATH TYPE

STABILITY TYPE REPEAT TYPE

ANOTHER

(1) block (2) hive (3) loaf (4) pail

(5) snake (6) boat (7) pond  

 

STABILITY TYPE

DEMO

　 (1) red light 　 (2) beacon 　 (3) clock

REPEAT TYPE

DEMO

(1) glider

(2) spaceship

ANOTHER

DEMO