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In order to demonstrate the efficiency of the proposed method, we calculate the
absolute and relative complexity. Then we rewrite the rules in compressed format.
For calculating absolute complexity, we count the length of the start and rule of each
grammar; then, let us relative complexity which is absolute complexity divided by
number of chars in Latin spelling of words. Therefore, we have absolute complexity
as follows:
•
Allah: Start (59), Rule (63)
•
Muhammad: Start (91), Rule (102)
•
Ali: Start(53), Rule (59)
And, the relative complexities are as follows:
•
Allah: Start (11.8), Rule (12.6)
•
Muhammad: Start (11.375), Rule (12.75)
•
Ali: Start(17.6666666667), Rule (19.6666666667)
Figure 12.15 shows these two kinds of complexities.
12.5
Conclusion
We design cellular automaton and L-Systems based algorithms for generating the
ancient Persian script Ma'qeli. We demonstrate how letters of the script can be pro-
duced using block cellular automata with Margolus neighborhood. We found a set
of optimal (in terms of generation time and richness of letters/words produced) rules
to generate complex Persian cursive words. The contribution towards this study has
a number of advantages, and has the capability of applying to several domains. First,
the script, as a graphical primitive, can be used in computer games and animations.
The script can also be used in industrial applications when displaying sentences in
7-segments or dot matrix monitors. We also envisage a possible usage in CAD soft-
ware in case of cultural heritages, handicrafts and the calligraphies woven through
the carpets. In order to demonstrate the efficiency of the proposed method, a set of
experiments is conducted on generating holy words 'Allah' and 'Muhammad' with
von Neumann, Moore, and Extended Moore neighborhoods so as to compare with
Margolus neighborhood. It was observed in the course of experiments that the pro-
posed method is simple for generating words and sentences, as it can produce each
letter with just one rule. In conclusion, it is worth mentioning that using L-Systems
can eliminate the overhead of constructing initial blocks in the proposed method.
References
1. Adamatzky, A., Bull, L.: Are complex systems hard to evolve? Complexity 14(6), 15-20
(2009)
2. Ahuja, M., Loeb, L.A.: Tessellations in Islamic calligraphy. Leonardo 28, 41-45 (1995)
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