1. Cellular Automata Pedro R. Andrade Tiago Garcia de Senna Carneiro
Gilberto Câmara
Münster, 2014

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

3. Cellular Automata (CA)
John von Neumann (December 28, 1903 – February 8, 1957) was a Hungarian mathematician, physicist and inventor.
1966. Theory of Self-Reproducing Automata,  Burks, A. W., ed., University of Illinois Press

4. Self-reproducing Automata
Much more than this. Build machine from raw energy!!!

5. Von Neumann’s CA Lattice of instances of a single machine (not cells)
4-adjacent stationary neighbourhood mapping the flow of information between the instances
Finite set of discrete states
Finite set of transition rules
Initial state
Discrete time (snapshots)

6. In Environmental Modelling …
A 2-dimensional cellular automaton consists of an finite grid of cells, each in one of a finite number of states.
CA_State( t ) = rules( CA_State( 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 }
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 to commit changes .

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 are too constrained to be useful
Extending the basic CA paradigm
States:
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
- discrete or continuous, deterministic of stochastic, etc
Neighborhood:
from a stationary 8-cell to generalized neighbourhood