Image Processing Reference
In-Depth Information
12.1
Introduction
According to Wolfram [9], there are no studies that cannot be modeled by cellu-
lar automata. Nowadays, the footstep of cellular automata, either synchronous or
asynchronous, can be found in different aspects of science [20] from modeling a
biological system [22] to produce a virtual social network [23]. Artificial models of
cellular development have been proposed over the years with the objective of un-
derstanding how complex structures and patterns can emerge from one or a small
group of initial undifferentiated cells [6]. This mathematical tool has the capability
of easing many proposed solutions and modeling them more intelligently.
On the other hand, an L-system (Lindenmayer system) is a parallel rewriting sys-
tem and a type of formal grammar. An L-system consists of an alphabet of symbols
that can be used to make strings, a collection of production rules that expand each
symbol into some larger string of symbols, an initial 'axiom' string from which to
begin construction, and a mechanism for translating the generated strings into ge-
ometric structures. Lindenmayer [12] used L-systems to describe the behavior of
plant cells and to model the growth processes of plant development. L-systems have
also been used to model the morphology of a variety of organisms [20] and can be
used to generate self-similar fractals such as iterated function systems.
In [11], 'Game of Life' with complex behaviors was characterized by simple syn-
chronous cellular automata's rules. The main contribution towards this work was to
design a simple set of rules to study the macroscopic behavior of a population.
The Firing Squad [10], Firing Mob [16], and Queen Bee [7] are other games in
which synchronization problems are investigated adequately. Piwonska and Sere-
dynski [19] studied the impact of utilizing genetic algorithm on extracting optimum
rules for 2D cellular automata. They utilized optimum extracted rules with von Neu-
mann neighborhood in order to reconstruct several patterns. Chavoya et al. [5] con-
sider the problem of growing a solid French flag pattern in a 3D virtual space. They
proposed an artificial development model for 3D cell pattern generation based on
CAs. Cell replication is controlled by a genome consisting of an artificial regula-
tory network and a series of structural genes. The genome was evolved by a genetic
algorithm in order to generate 3D cell patterns through the selective activation and
inhibition of genes. Morphogenetic gradients were used to provide cells with posi-
tional information that constrained cellular replication in space.
Bentley et al. [4] describe a novel computer simulation that uses evolution to ex-
hibit some of the functions of cell walls raphid pennate diatom valves. The model
of valve morphogenesis used was based on theories that highlight the importance of
cytoskeletal elements in valve development. An 'organic' negative imprint is grown
in a grid-based system, using both local and global rules to dictate grid cell states.
Silica then diffuses out into all remaining grid cells. At each stage of development
the generated valves were consistent with observations on real diatom valve growth.
Simulated models are extremely useful for investigating, visualizing, and develop-
ing theories of morphogenesis. It is the intention of this work to inspire further
model-based experiments and to try to bridge the gap between the disparate fields
of computer science and biology for the exploration of morphogenesis. This model
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