Pattern Formation Using Cellular Automata and L-Systems: A Case Study in Producing Islamic Patterns - Cellular Automata in Image Processing and Geometry - page 231

Fig. 12.3 Persian alphabet letters in Ma'qeli script [21]. The dashed lines show the base lines
of each letter.

or triangles. The orthogonal neighbors within squares are called the von Neumann
neighborhood (Fig. 12.4a), and those plus the diagonal neighbors are called the
Moore neighborhood (Fig. 12.4b and Fig. 12.4c). An alternative is the Margolus
neighborhood, which is used in Block Cellular Automata [17], and is implemented
with two n n-cell blocked square tessellations. These two square tessellations are

offset from each another by one row and one column. Fig. 4d visualizes a specific
kind of Margolus neighborhood in which each block consists of 2

×

× 2-cell tessella-

tions.

12.3 Proposed Method

As is previously mentioned, letters, words, and sentences expand in two-dimension
and this demand inspires us to utilize 2D cellular automata. Since it is important
to establish a trade-off between the form of patterns and the number of produc-
tive rules, block cellular automata are utilized by dividing the lattice of cells into