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The Shape of Math R09

The Shape of Math R09. VOL.1 The Life Game. 10 ． ０ 6 ． ０ 3 Masashi SANAE. What is The Life Game ?. 1970 John Horton Conway Mathematician, Cambridge University Simulation game The symbol of the biological society

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The Shape of Math R09

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  1. TheShapeofMathR09 VOL.1TheLifeGame 10．０6．０3 MasashiSANAE

  2. What is TheLife 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

  3. 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

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

  5. Example • Survival ： If N = 2 or 3 • Death ： If N <= 1 or N>=4 • Birth ： There isn’t a cell on “P” and N=3 1st generation 2nd generation × × 0 × × ×

  6. Example • Survival ： If N = 2 or 3 • Death ： If N <= 1 or N>=4 • Birth ： There isn’t a cell on “P” and N=3 1st generation 2nd generation 0 0 0 0 0

  7. Example • Survival ： If N = 2 or 3 • Death ： If N <= 1 or N>=4 • Birth ： There isn’t a cell on “P” and N=3 1st generation 2nd generation × × × × × 1 × ×

  8. Example • Survival ： If N = 2 or 3 • Death ： If N <= 1 or N>=4 • Birth ： There isn’t a cell on “P” and N=3 1st generation 2nd generation × × × × × 2 ×

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

  10. Example • Survival ： If N = 2 or 3 • Death ： If N <= 1 or N>=4 • Birth ： There isn’t a cell on “P” and N=3 1st generation 2nd generation ● 2 1 ● 1 ● 3 3 4 2 ● 2 1 3 ● 5 8 4 3 ● 1 ● 3 3 ● 4 2 ● 2 0 1 2 3 ● 2 1

  11. Example • Survival ： If N = 2 or 3 • Death： If N <= 1 or N>=4 • Birth： There isn’t a cell on “P” and N=3 2nd generation 3rd generation

  12. 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

  13. Let’s Try!

  14. Let’s Try!

  15. Death Type Patern Of Life STABILITY TYPE Repeat type Another

  16. STABILITY TYPE

  17. repeat TYPE

  18. Another (1) glider (2) spaceship

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