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Cellular automata

Y
Yang Yeeun

This document discusses Brian P. Hoke's 1996 work on cellular automata. It covers topics such as recursive and explicit sequence definitions, one-dimensional and two-dimensional cellular automata rules and examples, aspects of cellular automata in art including their similarity to Impressionist paintings, and how to create cellular automata art by establishing initial conditions and rules of propagation. The goal is to explore both the mathematical and artistic applications of these self-replicating systems.

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Brian P.Hoke 1996 Introduction Sequences: recursive and Explicit Definitions One-Dimensional Cellular Automata Two-Dimensional Cellular Automata Aspects of Cellular Automata in Art Creating Cellular Automata Art Conclusion 1
1.Introduction Von Neumann & Stanislaw Ulam 覓狩 1 0 2 5 伎 0 1 0 1 瑚概覈 1 0 1 2 覲旧螳ル蟲 7 4 0 3 襦覺螻牛 .. <Array of Cells> Ulams grid was an example of cellular automation. 2
1.Introduction Von Neumanns Self-Replicating Automation 0 0 0 1 0 1 0 0 1 0 1 o 0 0 0 0 3
Sequences: Recursive and Explicit Definitions Recursive sequences The simplest mathematical example of the information-transmission property of Cellular Automata is a recursively defined sequences. Sn=2Sn-1 A typical recursive rule S1=1 S:1,2,4,8,16,32.. Local(Domino) Sn=(2)n-1 Global S:1,2,4,8,16,32.. 4
3.One-Dimensional Cellular Automata 1-D is the simplest type of CA 0 0 0 0 1 0 0 0 0 The Sierpinski triangle 5
3.One-Dimensional Cellular Automata 1 update 1 1 1 update 1 1 0 1 1 Update 1 1 1 1 1 6
3.One-Dimensional Cellular Automata 0 times 1 1 times 1 2(1+1) 1 2 times 1 4(2+(1+1)) 6(1+2+2+1) 4(2+(1+1)) 1 7
3.One-Dimensional Cellular Automata -Sierpinski triangle 0 0 0 0 1 0 0 0 0 The same Initial condition Figure1 and Rule. But.. 0 0 1 0 1 0 0 1 0 Figure2 8
4.Two Dimensional Cellular Automata -Stepping stone rule The Elements of sequence-> Numbers The Elements 1-D CA-> Row of Cells The Elements 2-D CA-> Planes of Cells Figure1 Figure2 1~256 colors After apply the rule repeatedly 9
4.Two Dimensional Cellular Automata -Stepping stone rule Generate random number between 0 and 1 0.5 0.2 0.5 Generate random number between 0 and 1 0.7 0.2 0.7 Generate random number between 0 and 1 Game of life, Population genetics.. 10
5.Aspects of Cellular Automata in art Cellular Automata and Impressionism Camille Pissarro(Impressionist,1830~1903) Sunset at St. Charles, Eragny Young Peasant Girl Wearing a Hat 11
5.Aspects of Cellular Automata in art Cellular Automata and Impressionism る襷 蠏碁殊 讌 磯 螳 血 . 蠍磯 豌伎 譟壱襯 企 觜 蟆螻螻 覿覈蟆 蟆一豌企 語螻 . れ 襷豺 るΜ 螳 觜 讌豌 覲伎碁. 12
5.Aspects of Cellular Automata in art Cellular Automata and Impressionism Scanned image Scanned image + Stepping Stone Impressionism(Seurat) 13
6.Creating Cellular Automata Art Inspiration: A mental picture of the Big Bang, the creation the universe. 0 1 2 (A limited number of particle and a rule of propagation.) Initial condition: A small square of four blocks. 14
6.Creating Cellular Automata Art If the sum is.. 0 1 2 3 4 Then the states of the block becomes 0 1 2 0 1 1 2 2 0(3) 1 0 1 1 0(3) 2 1 0(3) 0(3) 2 2 1 15
6.Creating Cellular Automata Art Randomly rotate each block Rings or Concentric squares 16
7.Conclusion The variety of application for which cellular automata. Deterministic and stochastic processes. Different result for every trial.(Stepping stone) Different initial condition and the length of times allow for great variety of result. Between Random and the Rule 17

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Cellular automata

  • 1. Brian P.Hoke 1996 Introduction Sequences: recursive and Explicit Definitions One-Dimensional Cellular Automata Two-Dimensional Cellular Automata Aspects of Cellular Automata in Art Creating Cellular Automata Art Conclusion 1
  • 2. 1.Introduction Von Neumann & Stanislaw Ulam 覓狩 1 0 2 5 伎 0 1 0 1 瑚概覈 1 0 1 2 覲旧螳ル蟲 7 4 0 3 襦覺螻牛 .. <Array of Cells> Ulams grid was an example of cellular automation. 2
  • 3. 1.Introduction Von Neumanns Self-Replicating Automation 0 0 0 1 0 1 0 0 1 0 1 o 0 0 0 0 3
  • 4. Sequences: Recursive and Explicit Definitions Recursive sequences The simplest mathematical example of the information-transmission property of Cellular Automata is a recursively defined sequences. Sn=2Sn-1 A typical recursive rule S1=1 S:1,2,4,8,16,32.. Local(Domino) Sn=(2)n-1 Global S:1,2,4,8,16,32.. 4
  • 5. 3.One-Dimensional Cellular Automata 1-D is the simplest type of CA 0 0 0 0 1 0 0 0 0 The Sierpinski triangle 5
  • 6. 3.One-Dimensional Cellular Automata 1 update 1 1 1 update 1 1 0 1 1 Update 1 1 1 1 1 6
  • 7. 3.One-Dimensional Cellular Automata 0 times 1 1 times 1 2(1+1) 1 2 times 1 4(2+(1+1)) 6(1+2+2+1) 4(2+(1+1)) 1 7
  • 8. 3.One-Dimensional Cellular Automata -Sierpinski triangle 0 0 0 0 1 0 0 0 0 The same Initial condition Figure1 and Rule. But.. 0 0 1 0 1 0 0 1 0 Figure2 8
  • 9. 4.Two Dimensional Cellular Automata -Stepping stone rule The Elements of sequence-> Numbers The Elements 1-D CA-> Row of Cells The Elements 2-D CA-> Planes of Cells Figure1 Figure2 1~256 colors After apply the rule repeatedly 9
  • 10. 4.Two Dimensional Cellular Automata -Stepping stone rule Generate random number between 0 and 1 0.5 0.2 0.5 Generate random number between 0 and 1 0.7 0.2 0.7 Generate random number between 0 and 1 Game of life, Population genetics.. 10
  • 11. 5.Aspects of Cellular Automata in art Cellular Automata and Impressionism Camille Pissarro(Impressionist,1830~1903) Sunset at St. Charles, Eragny Young Peasant Girl Wearing a Hat 11
  • 12. 5.Aspects of Cellular Automata in art Cellular Automata and Impressionism る襷 蠏碁殊 讌 磯 螳 血 . 蠍磯 豌伎 譟壱襯 企 觜 蟆螻螻 覿覈蟆 蟆一豌企 語螻 . れ 襷豺 るΜ 螳 觜 讌豌 覲伎碁. 12
  • 13. 5.Aspects of Cellular Automata in art Cellular Automata and Impressionism Scanned image Scanned image + Stepping Stone Impressionism(Seurat) 13
  • 14. 6.Creating Cellular Automata Art Inspiration: A mental picture of the Big Bang, the creation the universe. 0 1 2 (A limited number of particle and a rule of propagation.) Initial condition: A small square of four blocks. 14
  • 15. 6.Creating Cellular Automata Art If the sum is.. 0 1 2 3 4 Then the states of the block becomes 0 1 2 0 1 1 2 2 0(3) 1 0 1 1 0(3) 2 1 0(3) 0(3) 2 2 1 15
  • 16. 6.Creating Cellular Automata Art Randomly rotate each block Rings or Concentric squares 16
  • 17. 7.Conclusion The variety of application for which cellular automata. Deterministic and stochastic processes. Different result for every trial.(Stepping stone) Different initial condition and the length of times allow for great variety of result. Between Random and the Rule 17