Cellular automata

Cellular automata

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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
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  1.Introduction  Von Neumann& Stanislaw Ulam 생물학의 1 0 2 5 수학적 해석 0 1 0 1 인공생명 1 0 1 2 복제가능도구 7 4 0 3 로봇공학 .. <Array of Cells> Ulam’s grid was an example of cellular automation. 2
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  1.Introduction  Von Neumann’sSelf-Replicating Automation 0 0 0 1 0 1 0 0 1 0 1 o 0 0 0 0 3
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  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
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  3.One-Dimensional Cellular Automata 1-Dis the simplest type of CA 0 0 0 0 1 0 0 0 0 The Sierpinski triangle 5
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  3.One-Dimensional Cellular Automata 1 update 1 1 1 update 1 1 0 1 1 Update 1 1 1 1 1 6
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  3.One-Dimensional Cellular Automata 0times 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
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  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
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  4.Two Dimensional CellularAutomata -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
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  4.Two Dimensional CellularAutomata -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
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  5.Aspects of CellularAutomata in art Cellular Automata and Impressionism Camille Pissarro(Impressionist,1830~1903) Sunset at St. Charles, Eragny Young Peasant Girl Wearing a Hat 11
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  5.Aspects of CellularAutomata in art Cellular Automata and Impressionism 색 점들로만 뒤 덮인 그림은 선을 전혀 사용하지 않았는데도 형태가 뚜렷이 나타난다. 점의 크기는 전체와 조화를 이룬다 빛을 견고하고 분명하게 결정체로서 인식하고 표현했다. 점들은 마치 흔들리듯 강렬한 빛의 움직임처럼 보인다. 12
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  5.Aspects of CellularAutomata in art Cellular Automata and Impressionism Scanned image Scanned image + Stepping Stone Impressionism(Seurat) 13
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  6.Creating Cellular AutomataArt 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
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  6.Creating Cellular AutomataArt 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
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  6.Creating Cellular AutomataArt Randomly rotate each block Rings or Concentric squares 16
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  7.Conclusion •The variety ofapplication 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