Transcript Low-carbon growth in Brazil?

Cellular Automata
Spatio-Temporal Information for Society
Münster, 2013
System Theory
Advantages
 Simple representation of the world
 Visual representation
 Modular and hierarchical
Disadvantages
 No heterogeneity
 Implicit spatial representation
 Fixed connections between stocks
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.
Self-replicating Automata
Basic Cellular Automaton
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Grid of cells
Neighbourhood
Finite set of discrete states
Finite set of transition rules
Initial state
Discrete time
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.
Neighborhood and Rules
Neighbourhood
Rules
Space and Time
t
States
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)
9
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.
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 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