Cellular automata and agent base models for urban studies: from pixels to cells to hexa-dpi's - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 316

tend to be more important at a timescale of weeks to months.
At the same time people move freely, or even independently, of
space (grid) while land uses tend to be heavily dependent on local
characteristics.
By integrating CA-cell based models (spatial models) and
ABMit will be possible to representmore realistic processes where
spatial/land and a-spatial/socioeconomic dynamics interact and
produce the feedbacks that re-produce emergent and complex
land changes. In order to achieve this integration goal one of the
primary tasks will be to solve the different data-structures and
data requirements of the two model types.
Urban land dynamics are self-organizing, stochastic, catas-
trophic and chaotic (i.e., Barredo et al . 2003; Batty 1997; Silva,
2004; Silva and Clarke 2005; de Roo and Silva, 2010). Spatial
and temporal dynamics are two important driving forces of the
complex adaptive process. The key to integrating new computa-
tional approaches into urban dynamic models is to understand
the interaction and synchronization of spatial and temporal pro-
cesses, and presenting innovative solutions of scalability effects
(i.e., MAUP effects - Martinez, Viegas and Silva, 2009; and Wu
and Silva's spatial/temporal synchronization tables, 2010).
The obvious question is: is this possible? A straight forward
answer would be: Yes - it already exists: (1) we have the com-
putational capabilities; (2) we have the modeling technology
studied and understood (for instance we are now coupling mod-
eling approaches to common platforms of GA and CA); (3) we
are now exploring massive amounts of data and unveiling new
relations and new models; (4) we have personnel from different
fields working together (increasing multidisciplinarity).
Remote sensing can/will play an important role for two main
reasons: (1) as the main input data source into the spatial
dimension (though satellites that scan the surface of the earth),
and into the a-spatial dimension (using other satellites that
capture the movement of mobile agents in shorter time spans
and link it with GA base models); (2) as a base aggregator where
spatial and aspatial dimensions find a common environment/
platform.
What would be the new data structure that would link
CA, ABM, GA - that would integrate matrix and vector data
structures, spatial and aspatial dimensions in a dynamic evolving
self-organizing environment.
The hexa-dpi structure has the potential to overcome some
of the existent limitations, by proposing a new hexagonal spatial
matrix that will work as the ''virtual'' magnetic field where
spatial cell-based-dots can move freely and aggregate, vary its
dependence on local and global intervention, and exist as a
material entity or as an immaterial attribute. No hexagonal-cell
will be ''empty'' at any point of space, the scale of analysis and
units will play an important role in defining the objects capable
to observe/classify.
Figure 22.6 synthesizes some of the main characteristics of
the hexa-dpi structure and its associated cellular and agent's
environment. In the figure, box. 6.1 represents the basic struc-
ture (that was simplified for the purpose of this chapter), it
should be approximately hexagonal, doesn't need to be a physical
representation as such, but will be a fluid physical reference (a
kind of magnetic field where other structures will congregate
accordingly to the dimension of the net); still as part of the cellu-
lar/spatial environment the dots represent an important addition
(explored in box. 6.2) they have different sizes and will have
higher/lower mobility depending of the scale and unit of analysis

(they are mutable/transformable, never disappearing only chang-
ing to lower/higher scales/nets). The interplay of the hexagonal
structure and dots in the 'cellular environment' will grant among
other things, scalability. Finally, Figure 22.6.3 represents the
'materialization' of some of the spatial features into objects that
can be identified by us as recognizable objects, allowing classifiers
of objects to embed attributes into the hexa-dpi structure and
build objects (i.e. cars, houses, urban land uses, farmland).
In a way we are coming full circle, from initial dots in
a picture, to rigid pixel-matrix structures and its associated
deterministic models, to more flexible, changing and emergent
behaviours of cells and agents and their initial stochastic models.
To today's hybrid models that have the goal of aggregating the
benefits of both worlds. The future requires full integration of
spatial-aspatial data structures.

Conclusions

Computers and the opportunities derived from computation
allowed the application or simultaneous development of new
theories. What is now known as the study of complexity has
its roots during the 1950s. Pre and post Second World War
developments allowed remote surveying of the land, first as
photos of dots per inch, latterly as pixels in a matrix, scanned
from satellites. These vast matrixes with an individual number
per pixel were important not only to analyze existent data
but to derive new data. With time deterministic analysis gave
place to probabilistic analysis and more complex data mining
techniques that needed to rely on more elaborate algorithms.
The acknowledgment that stochastic analysis could be more
accurate in the representation of the phenomena, allowed the
development of CA models and GA/ABM models. In turn, the
observation that real life does not separate aspatial and spatial
patterns and processes is now directing new developments in
modeling that avoid the spatial vs. aspatial divide and this
requires newdatamodels and newdata structures (termed here as
hexa-dpis).

References

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