Representing Geographic Phenomena with Cellular Automata

1. Autômatos Celulares Disciplina SER 301 Análise Espacial de Dados Geográficos Líliam C. Castro Medeiros lccastro@dpi.inpe.br Raian Vargas Maretto raian@dpi.inpe.br

2. Como representar computacionalmente fenômenos geográficos?

3. Como representar computacionalmente fenômenos geográficos? Itaituba – PA (1985). TM/Landsat-5 composition R(3) G(2) B(1). Source: INPE image catalog Escala temporal? Source: Fred Ramos

4. Como representar computacionalmente fenômenos geográficos? Fonte: PRODES/INPE Modelos baseados em Autômatos Celulares

5. Cellular Automata • Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

6. Cellular Automata • Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

7. Cellular Automata • Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

8. Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

9. Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

10. Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

11. Dynamic and self-reproducing sistems • Discrete space and time • The basic elements: cells The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

12. Each cell contains: • A finite set of predeterminated states • A set of transition rules (to change the states) which depend on the cell’s neighborhood The nth iteration Neumann JV, Burks AW (1966). The Theory of Self-Reproducing Automata, University of Illinois Press, Urbana

13. Source: Rita Zorzenon’s slide

14. The Cellular Automata Desenvolvido pelo matemático húngaro John von Neumann, que na década de 40, propôs um modelo baseado na ideia de sistemas lógicos que fossem auto-reprodutores e que imitassem a própria vida. Cooper NG (1983). From Turing and von Neumann to the present. Los Alamos Science.

15. Source: Carneiro, 2006 Ex: Attribute Land Use: f (It) f (It+2) f (It+1) f ( It+n ) • Possible States: • Forested • Agriculture • Urban F F . . . Transition rule based an modeler defined function Source: Gilberto Câmara.

16. Forecast tp + 10 Calibration Calibration Dynamic Spatial Models tp - 20 tp - 10 tp Source: Cláudia Almeida

17. An Example: John Conway’s Game of Life • a regular grid with square cells

18. An Example: John Conway’s Game of Life • each cell can be white (alive) or black (dead)

19. An Example: John Conway’s Game of Life • each cell can be white (alive) or black (dead) • for each cell, their neighbors are the 8 closer cells Figure: Leonardo Santos et al. (2011). A susceptible-infected model for exploring the effects of neighborhood structures on epidemic processes – a segregation analysis. Proceedings XII GEOINFO, November 27-29, 2011, Campos do Jordão, Brazil. p 85-96.

20. An Example: John Conway’s Game of Life • eachcellcanbewhite (alive) orblack (dead) • for eachcell, theirneighbors are the 8 closercells • ateach time step, thestateofeachcellobeythefollowingrules (executedsimultaneously): • thecellsurvivesifthere are 2 or 3 aliveneighborcells, otherwisethecelldies • a diedcellcanchange to analivecellif it hasexatly 3 aliveneighbors, otherwise it remainsdead

21. Game ofLife John Conway (1970) Possible states: alive or dead • Death: • by loneliness - one or zero neighbors • by overpopulation – more than 4 neighbors • Birth: cells with exactly 3 alive neighbors • Survival: exactly 2 or exactly 3 alive neighbors Adapted from Adriana Racco’s slide

22. Rita Zorzenon’s slide

23. Mas a saída são só essas figurinhas? Não consigo ver a coisa acontecendo?

24. Game of Life Some sites to see the Game of Life simulation: http://www.terrame.org/doku.php?id=examples http://www.math.com/students/wonders/life/life.html http://www.bitstorm.org/gameoflife/

25. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

26. The Grid

27. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

28. The GeometryExample: Two-DimensionalGrids with regular Cells Cells that have a common edge with the involved are named as “main neighbors” of the cell (are showed with hatching) The set of actual neighbors of the cell a, which can be found according to N, is denoted as N(a) Source: Lev Naumov’ slide

29. Irregular Spaces Cell Polygons Lines Points

30. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Adapted from Leonardo Santos’ slide

31. Vizinhanças • Componente essencial nos modelos baseados em AC • Determinam como os elementos do modelo interagem entre si • Duas células são vizinhas se uma exerce alguma influência sobre o estado da outra Fonte Slide: Adaptado de Maretto, 2011 Fonte Fig.: (ANDRADE-NETO et al., 2008)

32. Von Neumann Neighborhood First neighbors Second neighbors Adapted from Adriana Racco’s slide

33. Moore Neighborhood First neighbors Second neighbors Adapted from Adriana Racco’s slide

34. Random Neighborhood Adapted from Adriana Racco’s slide

35. Other Neighborhoods The arbitrary neighborhood is determined by the model Examples: Based on people activity-space (Santos et al, 2011) First neighbors Second neighbors Based on data (Aguiar et al, 2003) Adapted from Adriana Racco’s slide

36. Neighborhoods in Time • They can be • static: the same neighbors all the time (classical CA) • dynamic: the neighbors can change at each time step

37. Neighborhoods in Time Rondônia - 1986 Rondônia 1975 Ocupação Humana [Câmara et al., 2009]

38. Neighborhoods in Time Source: Adapted from Maretto, 2011

39. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

40. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

41. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

42. Rules • The rules may depend on the state of the own cell neighbor’s cells • The rules may be based on influence fields of the geography of the system • They may be deterministic or stochastic • They can depend only on the actual state of the cells Adapted from Adriana Racco’s slide

43. CA = (G, N, S, IC, R, BC, UC) G: Geometry N: Neighborhood S: States IC: Initialcondition R: Rules BC: Boundaryconditions UC: Updatingcriteria The CA Structure Source: Adapted from Leonardo Santos’ slide

44. Boundary Conditions • Periodic (1D - ring or 2D – torus)

45. Boundary Conditions • Periodic (1D - ring or 2D – torus)

46. Boundary Conditions • Periodic (1D - ring or 2D – torus)

47. Boundary Conditions • Periodic (1D - ring or 2D – torus)

48. Boundary Conditions • Periodic (1D - ring or 2D – torus) • Reflexive

49. Boundary Conditions • Periodic (1D - ring or 2D – torus) • Reflexive • Fixed

50. Boundary Conditions • Periodic (1D - ring or 2D – torus) • Reflexive • Fixed • Null (the cells located on the borders have as neighbors only those cells immediately adjacent to them into the grid) • Others