The Shape of Math R09 VOL.3 The Life Game ０９．０８．０ ４ Masashi SANAE

What is The Life Game ?  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

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 time

Example × ●●● ●●● ●●● 1st generation2nd generation × ×× 0 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation ×× × 0 ×× Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation ××× 1 × ×× × Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation ××× 2 × × × Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation ××× 3 ×× ● Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3

Example × ●●● ●●● ●●● 1st generation2nd generation 21 1 ● ● 3 ● 3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 42● ● ● ● ●● ●

Example ● ●●● ●● ●●● ● 2nd generation rd generation Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 Survival ： If N = 2 or 3 Death ： If N =4 Birth ： There isn’t a cell on “P” and N=3 ●● ●●●● ●●● ●●●● ●●

Let’s Try! ●●● ● ●● ● Exercise 1 Exercise 2

Answer 1 ●●● 1st generation ● ● ● 2nd generation ●●● 3rd generation

Answer 2 1st generation2nd generation3rd generation ● ●● ● 4th generation ●● ●● ●● ●● ●● ●●

(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