Cellular Automata Spatio-Temporal Information for Society Münster, 2013.
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Transcript of Cellular Automata Spatio-Temporal Information for Society Münster, 2013.
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Cellular Automata
Spatio-Temporal Information for Society
Münster, 2013
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System Theory
AdvantagesSimple representation of the worldVisual representationModular and hierarchical
DisadvantagesNo heterogeneityImplicit spatial representationFixed connections between stocks
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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.
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Self-replicating Automata
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Basic Cellular Automaton
Grid of cells Neighbourhood Finite set of discrete states Finite set of transition rules Initial state Discrete time
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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.
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Neighborhood and Rules
RulesNeighbourhood
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.
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www.terrame.org
“CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena”(Mike Batty)
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9
Source: Rita Zorzenon
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Game of life
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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)
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Neighborhood A Neighborhood represents the proximity relations
of a cell.
world:createNeighborhood{
strategy = "moore",self = false
}
Von Neumann Moore
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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”}
}}
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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.
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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;
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Which Cellular Automata?
For realistic geographical modelsthe basic CA principles too constrained to be useful
Extending the basic CA paradigm From binary (active/inactive) values to a set of
inhomogeneous local statesFrom 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 neighbourhoodFrom system closure to external events to external output
during transitions