Pattern Formation Using Cellular Automata and L-Systems: A Case Study in Producing Islamic Patterns - Cellular Automata in Image Processing and Geometry - page 232

Fig. 12.4 Topologies analyzed in the paper are (a) squares with the von Neumann neigh-
borhood, (b) squares with the Moore neighborhood, (c) squares with the extended Moore
neighborhood, and (d) the Margolus neighborhood

non-overlapping blocks. Block cellular automata are useful for generating Ma'qeli
scripts, since they are straightforward to choose transition rules that obey writing
laws and apply them simultaneously and synchronously to a whole block at a time
rather than a single cell. In view of the fact that synchronous cellular automata si-
multaneously apply all transition rules to all blocks, the procedure of script genera-
tion encounters serious problems. In order to achieve a correct script generation, we
have to be aware of the fact that each rule must be executed in a correct time step.
Not only does this type of supervision make rule extraction process difficult, but also
it is impossible in some cases. Therefore, in present study we use asynchronous cel-
lular automata to ease both the pattern formation and the rule extraction process.

12.3.1 Ma'qeli Character Generation Using Margolus

Neighborhood

The proposed block scheme consists of Margolus neighborhood itself in which
the lattice is divided into 3 3-cell blocked square tessellations, in as much as all

Ma'qeli characters can be bounded by such block (Fig. 12.5). An extension to a
standard Margolus neighborhood is proposed which does not need to be shifted by
one cell on alternate timestamps and can generate preferable patterns in one times-
tamp. As shown in Fig. 3, 64 characters are just defined without any additional

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