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The Shape of Math

The Shape of Math. The Life Game. 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

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  1. TheShapeofMath TheLifeGame 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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