1. Pedro R. Andrade Münster, 2013
Cellular Automata
Pedro R. Andrade
Münster, 2013

2. System Theory Advantages Disadvantages
Simple representation of the world
Visual representation
Modular and hierarchical
Disadvantages
No heterogeneity
Implicit spatial representation
Fixed connections between stocks

3. Cellular Automata
Firstly developed by Hungarian mathematician John von Neumann, who proposed a model based on the idea of ​​logical systems that were self-replicating.

4. Self-replicating Automata

5. Basic Cellular Automaton
Grid of cells
Neighbourhood
Finite set of discrete states
Finite set of transition rules
Initial state
Discrete time

6. 2-Dimensional Automaton
A 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.

7. Neighborhood and Rules
Neighbourhood
States
Space and Time t t1
Each cell is autonomous and change its state according to its current state and the state of its neighborhood.

8.
“CAs contain enough complexity to simulate surprising
and novel change as reflected in emergent phenomena”
(Mike Batty)

9. Source: Rita Zorzenon

10. Game of life

11. CellularSpace A CellularSpace is a set of Cells.
It consists of an area of interest, divided into a regular grid.
world = CellularSpace{
xdim = 5,
ydim = 5 }
forEachCell(world, function(cell)
cell.value = 3
end)

12. Neighborhood
A Neighborhood represents the proximity relations of a cell.
world:createNeighborhood{
strategy = "moore",
self = false } X y
Von Neumann
Moore

13. Legend
Defines colors to draw the Cells of a CellularSpace. Can be used with map observers. coverLeg = Legend { grouping = "uniquevalue", colorBar = { {value = 0, color = "white"}, {value = 1, color = "red"}, {value = 2, color = "green”} }

14. Synchronizing a CellularSpace
TerraME can keep two copies of a CellularSpace in memory: one stores the past values of the cells, and another stores the current (present) values of the cells.
The model equations must read the past copy and write the values to the present copy of the cellular space.
At the correct moment, it will be necessary to synchronize the past copy with the current values of the cellular space.

15. 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;

16. 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