1. Análise Espacial de Dados Geográficos
Autômatos Celulares
Disciplina SER 301
Análise Espacial de Dados Geográficos
Líliam C. Castro Medeiros

2. 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

3. 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

4. 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

5. 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. 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. 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. 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

10. Source: Rita Zorzenon’s slide

11. 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.

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

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

14. 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

15. 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
at each time step, the state of each cell obey the following rules (executed simultaneously):
the cell survives if there are 2 or 3 alive neighbor cells, otherwise the cell dies
a died cell can change to an alive cell if it has exatly 3 alive neighbors, otherwise it remains dead

16. Possible states: alive or dead
Game of Life
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

17. Rita Zorzenon’s slide

18. Game of Life Some sites to see the Game of Life simulation: or

19. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

20. The Grid

21. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

22. The Geometry Example: Two-Dimensional Grids
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

23. Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Adapted from Leonardo Santos’ slide

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

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

26. Adapted from Adriana Racco’s slide
Random Neighborhood
Adapted from Adriana Racco’s slide

27. 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

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

29. when: December, 12th, at 2 p.m.!
where: IAI auditorium

30. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

31. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

32. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

33. Adapted from Adriana Racco’s slide
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

34. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

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

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

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

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

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

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

41. 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

42. Source: Adapted from Leonardo Santos’ slide
CA = (G, N, S, IC, R, BC, UC)
G: Geometry
N: Neighborhood
S: States
IC: Initial condition
R: Rules
BC: Boundary conditions
UC: Updating criteria
The CA Structure
Source: Adapted from Leonardo Santos’ slide

43. Examples of Bidimensional Cellular Automata Models

45. You can also see this in
sites.google.com/site/amazonida/drops/forestfire

46. Other Example of
Cellular Automata Model

47. Dengue Fever
It is a viral disease trasmitted in Brazil mainly by Aedes aegypti mosquito

48. Stages of Infection In Mosquitoes Susceptible Infected
8 to 12 days
Susceptible
Infected
Extrinsic
Incubation
Period
time
Mosquito infects humans
Moment of
infection
Figure:
Whitehead SS, Blaney JE, Durbin AP, Murphy BR (2007). Prospects for a dengue virus vaccine. Nature Reviews Microbiology, 5:

49. Dengue Stages In Humans Susceptible Infected Recovered time Intrinsic
Incubation
Period
Contagious
Human
infects mosquitoes
Moment of
infection
3 to 14 days
Average between
4 and 5 days
Average between
4 and 7 days
Figure:
Whitehead SS, Blaney JE, Durbin AP, Murphy BR (2007). Prospects for a dengue virus vaccine. Nature Reviews Microbiology, 5:

50. There are four distinct serotypes of the virus:
Dengue Virus
There are four distinct serotypes of the virus:
DENV1, DENV2, DENV3 e DENV4

51. The Model

54. A multi-level stochastic cellular automata
Humans
Mosquitoes
A multi-level stochastic cellular automata

55. The Model
Humans
Mosquitoes

56. The Model
Humans
Mosquitoes

57. The Model
Time of
infection
(days)
State
Humans
Mosquitoes

58. The Model
Humans
Mosquitoes
Time of
infection
(days)
Age
days

59. Patterns

60. Model Considerations Human mobility Asymptomatic people Human renewal
House infestation
Vector density per household
Each iteration corresponds to a day
Periodic boundary conditions

61. Simulation in Human Lattice
Inicialmente:

62. Simulation in Mosquito Lattice
Inicialmente:
Um único
humano infectado

63. Parameters of the Model
Human occupation rate
Number of humans at each residence
Human/vector population radio
House infestation rate
Daily bite frequency
Incubation periods
Contagious period
Mosquito daily survival probability
Contamination probabilities

64. Other Example of Cellular Automata Model

65. Source: Leonardo Santos and Suani Pinho

66. Source: Leonardo Santos and Suani Pinho

67. Source: Leonardo Santos et al (2009)

68. Patterns Generated by Cellular Automata Models
Rita Zorzenon’s slide

69. Patterns Generated by Cellular Automata Models
Rita Zorzenon’s slide

70. TerraME www.terrame.org
Is a programming environment for spatial dynamical
modeling. It supports cellular automata,
agent-based models and network models
running in 2D cell spaces.
It provides an interface to TerraLib geographical
database, allowing models direct access to
geospatial data.

72. Other Example chuva chuva chuva N Pico do Itacolomi do Itambé
Serra do Lobo N
Fonte: (Carneiro, 2006) 72

73. Cellular Automata WET DRY (soilWater > infCap) ?
Fonte: (Carneiro, 2006)

74. Simulation outcome
fonte:
Carneiro (2006)