Pattern Formation Using Cellular Automata and L-Systems: A Case Study in Producing Islamic Patterns - Cellular Automata in Image Processing and Geometry - page 236

initial state of the system, and P is a set of production rules or productions defining
the way variables can be replaced with combinations of constants and other vari-
ables. A production consists of two strings, the predecessor and the successor. For
any symbol 'A' in V which does not appear on the left hand side of a production in
P, the identity production A A is assumed; these symbols are called constants or

terminals. The rules of the L-system grammar are applied iteratively starting from
the initial state.
The grammars for producing 'Allah', 'Muhammad', and 'Ali' are as follows:

ₒ

Case Allah

Va r i a b l e s ='X';
Constants = 'F' 'f' '+' '-';
Start = '-FFFF-f-FFFF+f-F+f+F+F-fF-F-f-fffFF+FF-ffFF-FFFF+FF+FF+FFX'
Rules = 'X' '-ffffFFFF-f-FFFF+f-F+f+F+F-fF-F-f-fffFF+FF-ffFF-FFFF+FF+FF+FFX'
Angle = π /2;

Case Muhammad

Va r i a b l e s ='X';
Constants = 'F' 'f' '+' '-';
Start ='-FF+FF+FF+FFFFF-FF+FFF+Ff+FFF-fffFF-ffF-f-F-F+f+F+Ff-ffFF-FF-FF-FF-
ffFFF-FF+FF+ffff+FF+FFX'
Rules = '-FF+FF+FF+FFFFF-FF+FFF+Ff+FFF-fffFF-ffF-f-F-F+f+F+Ff-ffFF-FF-FF-FF-
ffFFF-FF+FF+ffff+FF+FFX'
Angle = π /2;

Case Ali

Va r i a b l e s ='X';
Constants = 'F' 'f' '+' '-';
Start ='++FF+FF+FF-ffFFF-FFF-fff-FF+FF+FF-FF-FFFFF-FFFFX'
Rules ='X' '-fffffff-FF+FF+FF-ffFFF-FFF-fff-FF+FF+FF-FF-FFFFF-FFFFX'
Angle = π /2;