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CELLULAR AUTOMATA Derek Karssenberg, Utrecht University, the Netherlands LIFE (Conway)

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Presentation on theme: "CELLULAR AUTOMATA Derek Karssenberg, Utrecht University, the Netherlands LIFE (Conway)"— Presentation transcript:

1 CELLULAR AUTOMATA Derek Karssenberg, Utrecht University, the Netherlands LIFE (Conway)

2 introduction Principle of cellular automata Local (spatial) interactions create global pattern of change Example: vegetation patterns localglobal

3 introduction Principle of cellular automata Local (spatial) interactions create global pattern of change Example: forest fire local

4 introduction Principle of cellular automata Local (spatial) interactions create global pattern of change Example: forest fire global

5 introduction Spatial discretization: regular lattice of cells

6 introduction Formulating cellular automata General case for dynamic spatial models: with: z k 1..k state variables i j 1..j inputs f k 1..k functionals

7 introduction Formulating cellular automata General case for dynamic spatial models: which can be rewritten as: zvector of state variables (was z k ), the ‘state of the cell’ ivector of inputs (was i j ) fnumber of functionals (was f k )

8 introduction Formulating cellular automata Cellular automata: no inputs (although in practice inputs may be used) all variables in z are classified (although scalars are sometimes used) f is a function (‘transition rule’) of a direct neighbourhood and the cell itself only the change from t to t + 1 is not a function of time What is f?

9 introduction Notation rules: referring to neighbouring cells the state of the cell on row i, column j

10 transition rules Transition rule: von Neumann Neighborhood

11 transition rules Transition rule: Moore neighborhood

12 transition rules Transition rule: extended von Neumann neighborhood

13 introduction Life, also known as Game of Life Developed by John Conway, 1970 One boolean variable: TRUE (= live cell) or FALSE (= dead cell) Uses the Moore neighborhood

14 introduction Life, also known as Game of Life Transition rules (i.e. f) a dead cell with exactly three alive neighbors becomes a live cell (birth)

15 introduction Life, also known as Game of Life Transition rules (i.e. f) a dead cell with exactly three alive neighbors becomes a live cell (birth) a live cell with two or three neighbors stays alive (survival)

16 introduction Life, also known as Game of Life Transition rules (i.e. f) a dead cell with exactly three alive neighbors becomes a live cell (birth) a live cell with two or three neighbors stays alive (survival) in all other cases, a cell dies or remains dead

17 introduction LIFE in PCRaster initial Alive=uniform(1) gt 0.5; dynamic NumberOfAliveNeighbors=windowtotal(scalar(Alive),3)- scalar(Alive); Alive=(NumberOfAliveNeighbors eq 3) or ((NumberOfAliveNeighbors eq 2) and Alive);

18 stochastic variables in PCRaster Demo game of life edit tot.mod display ini.map aguila –2 alive000.001+1000 test0000.001+1000

19 stochastic variables in PCRaster Self-organization Internal organization of a system increases in complexity without being guided by an input variable Emergent properties Complex pattern formation from more basic constituent parts or behaviors Example: game of life Many examples in ecology, sedimentology


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