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

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

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

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

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)

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) )

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.

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

Source: Rita Zorzenon

Game of life

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)

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

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"} }

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 .

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;

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