Image Processing Reference
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of diatom valve morphogenesis is interestingly similar to the negative technique
used by artists in batik painting.
In [13], scholars use cellular automata for modeling shell pigmentation of mol-
luscs. They found self-organization into stationary (Turing) structures, travelling
waves, chaos, and so-called class IV behavior during their research. Class IV be-
havior consists of a disordered spatio-temporal distribution of periodic and chaotic
patches, which differs from chaos in that it has no well-defined error propagation
rate. The calculations of the modes agree well with observations in natural shells.
Their results suggest evidence in nature for class IV behavior, a mode that had
so far been reported only as the result of simulations. Oya et al. [18] use single-
electron circuits to perform dendritic pattern formation with nature-inspired cellular
automata. They propose a novel semiconductor device in which electronic-analogue
dendritic trees grow on multilayer single-electron circuits. A simple cellular automa-
ton circuit was designed for generating dendritic patterns by utilizing the physical
properties of single-electron devices.
Another application of pattern formation, which is a highly demanded topic
among computer graphics researchers, is producing cultural-related motifs which
are still yet to mature due to their production complexities. Cellular automata show
their brilliant capability in this application too; as a result, much research has been
devoted to apply this mathematical tool for generating complex patterns [12]. Arata
et al. [3] made an effort on applying cellular automata with Margolus neighborhood
to model an interactive free-form scheme within a 3D Voxel space for designing vir-
tual clay objects. They assumed each Voxel is allocated a finite state automaton that
repeats state transitions according to the conditions of its neighbor Voxels. Type-
face and language's script are other attractive patterns, which entices researchers to
bring their utility and attractiveness into focus. Xu et al. used a computational ap-
proach to digital chinese calligraphy and painting [24]. Ahuja et al. [2] utilized a
number of geometric shapes to tessellate the 'Ali' pattern. In [15] a prototype for
performing geometrical transformations was introduced with the aim of decoration
designs by the Kufic square scripts. Ma'qeli script is a sort of ancient Persian script
with amazing features (refer to Fig.12.1); however, a small number of its patterns
were produced by Minoofam and Bastanfard [14] utilizing synchronous cellular au-
tomata.
This chapter will review the basic foundation of CAs and L-Systems in pattern
formation especially those which are related to the cultural heritage. Then, it will
be concentrated on generating all forms of the Ma'qeli script with CAs and three
holy Islamic words using L-Systems with two clear reasons which one of these is
decidedly more glamorous than the other one. The glamorous reason deals with the
distinctive features of Persian script, i.e., it is cursive, it depends on the base line,
and it is the formal writing typeface of more than 150 million people. All of this has
overshadowed the less glamorous side of the reason, which deals with the tessellated
nature of Ma'qeli script. This reason seems to have been shown more adaption with
cellular automata rather than geometric methods. The focus of this study is not only
on generating Ma'qeli script pattern utilizing 2D asynchronous cellular automata
and Margolus neighborhood, but also on finding optimum set of rules for this sort
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