1. Spatio-temporal information in society: cellular automata
Gilberto Câmara
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2. Computational Modelling with Cell Spaces
Components
Generalizes Proximity Matriz – GPM
Hybrid Automata model
Nested enviroment

3. Cell Spaces

4. Cellular Automata: Humans as Ants
Matrix,
Neighbourhood,
Set of discrete states,
Set of transition rules,
Discrete time.
“CAs contain enough complexity to simulate surprising
and novel change as reflected in emergent phenomena”
(Mike Batty)

5. 2-Dimensional Automata
2-dimensional cellular automaton consists of an infinite (or finite) grid of cells, each in one of a finite number of states. Time is discrete and the state of a cell at time t is a function of the states of its neighbors at time t-1.

6. Cellular Automata
Neighbourhood
Rules
Space and Time t
States t1

7. Most important neighborhoods
Von Neumann Neighborhood
Moore Neighborhood

8. Conway’s Game of Life
At each step in time, the following effects occur:
Any live cell with fewer than two neighbors dies, as if by loneliness.
Any live cell with more than three neighbors dies, as if by overcrowding.
Any live cell with two or three neighbors lives, unchanged, to the next generation.
Any dead cell with exactly three neighbors comes to life.

9. Game of Life
Static Life
Oscillating Life
Migrating Life

10. Conway’s Game of Life
The universe of the Game of Life is an infinite two-dimensional grid of cells, each of which is either alive or dead. Cells interact with their eight neighbors.

11. Characteristics of CA models
Self-organising systems with emergent properties: locally defined rules resulting in macroscopic ordered structures. Massive amounts of individual actions result in the spatial structures that we know and recognise;

12. Which Cellular Automata?
For realistic geographical models
the basic CA principles too constrained to be useful
Extending the basic CA paradigm
From binary (active/inactive) values to a set of inhomogeneous local states
From discrete to continuous values (30% cultivated land, 40% grassland and 30% forest)
Transition rules: diverse combinations
Neighborhood definitions from a stationary 8-cell to generalized neighbourhood
From system closure to external events to external output during transitions