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A Novel Algorithm for Generating an Islamic Pattern Based on Cellular Automata

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A Novel Algorithm for Generating an Islamic Pattern Based on Cellular Automata A Novel Algorithm for Generating an Islamic Pattern Based on Cellular Automata Seyed mir Hadi MinoofamA, 8am BastanfardAA AIslamic 8ad Bniversity of Ca8vin, minoofamDqa8viniau.ac.ir AAIslamic 8ad Bniversity of 5araj, bastanfardDkiau.ac.ir Abstract: Creating algorithmic approach for generating Islamic as square kufic or rectangular kufic, because its letters are patterns extends its applications in architectures, decoration and art. Researchers face with many challenges in developing like rectangles and squares and are often used in tiling algorithms such as providing a simple and applicable architectures. Ma'qeli is an rabic name refers to this fact algorithm to describe complex patterns. This paper used that the design and reading of these patterns require very cellular automata with extended Moor neighborhood to much thinking %12'. Ma'qeli script is based on square tiles generate Ma' eli script patterns. The proposed approach leads to accurate and scalable algorithm for generating words like chess cells and written using geometrical shapes like pattern. The joint and disjoint pattern shapes of the letters will squares, rhombuses, rectangles, parallel and intersecting be reserved in this approach. The results of implemented lines and usually with lack of points %1,'. 6ecause algorithms demonstrate our approach with a variety of Ma' eli Ma'qeli scripts are patterns based on square grids, patterns. therefore we can construct these patterns with cellular automata %15'%16'%11'. This paper describes a new Keywords: Cellular automata, Islamic patterns, Ma'qeli method for generating 3Muhammad3 pattern in Ma'qeli script, Non-photo realistic rendering, Pattern formation. script with cellular automata. 7e use extended Moore 1. Introduction neighborhood for managing letters effectively. The rest of the paper is organi8ed as follows. Section 2 Pattern formation based on algorithm is used in refers to some related works. Section , describes the basic computer graphics as non-photo realistic rendering. Non- notions of two dimensional cellular automata. Section . photo realistic rendering is a challenging field which provides a novel algorithm for generating 3Muhammad" includes modeling artificial and artistic things made by pattern using cellular automata. Techniques for creating humans. cellular automaton is a good algorithmic visually appealing designs are proposed in section 5. approach used for pattern generation. Its grid based Experimental results appear in section 6. The paper is property makes it suitable for executing tiling algorithms. concluded in section 1. Tiling or tessellation means filling a plane with a collection of shapes that are completely filled with no . Related Works overlapping or blank %1'. Tessellation is found in many Islamic art and calligraphy are branches of non-photo new and old architectural buildings and one of the most realistic rendering techniques. Rendering of Islamic famous is lhambra palace, Spain %6'. Ornamental geometry is one of the challenging tasks in computer geometry artisans have wonderfully decorated all surfaces graphics for example: Islamic geometry is used in many of the palace %2' %,'. lso in many artworks of designers countries in the world %2'. Recently, 5aplan offers an like Escher many beautiful patterns can be found %.' %5'. algorithm for generating Islamic star patterns based on These patterns have mathematical properties which make radially-symmetric motifs %12' %14'. Lu extracts some generating algorithm possible. Calligraphy is another symmetry in medieval Islamic tiling based on quasi- ancient art which creates many beautiful designs in crystalline %20'. ljamali et al., as well as Valor have different countries depending on the script commonly done researches on classifying Islamic geometrical used there. 0or Example, calligraphy was written with patterns %21'%22'. rabic scripts in many countries in the Middle East %1' lso many researches have been done for generating %2'. Even because of the close dependency between calligraphic patterns in Chinese %2,' %2.' %25', Japanese rabic calligraphy and geometry, the calligraphy was %26' as well as rabic scripts %21'. lthough Ma'qeli called 3geometry of script3 %4'. Therefore the calligraphy script is also a kind of Islamic geometry, unfortunately is based on geometry and mathematics as well, and we limited numbers of researches have concentrated on can generate algorithms for writing letters. One of the Ma'qeli script. huja and Loeb described the tessellation most important rabian scripts is the kufic script. 5ufic of the word 3 li3 in a hexagon %22'. Mostapha and script generally is angular and had written in different 5rishnamurti introduced a prototype for generating forms such as Ma'qeli form. Ma'qeli kufic is also known 431 calligraphic patterns, but they didnEt describe the way for Next section explains about transition rules for creating original pattern %24'. generating 3Muhammad3 pattern. Ma'qeli patterns are inserted in a geometrical field. In this script all letters are based on hori8ontal or vertical 4. Transition Rules for (Muhammad( Pattern lines with 40F angels. lthough there are many ways to create In this paper we generate calligraphic 3Muhammad3 3Muhammad3 pattern from artistic point of view, in this pattern using cellular automata. In comparison with section we extract some rules for generating , most previous algorithms, our algorithm is simpler, more famous models of 3Muhammad3 pattern. The word flexible and more scalable too. 3Muhammad3 formed by joint letters and in this word the some letters in joint form are as the same and this maybe 3. Two Dimensional Cellular Automata lead to same states for different cells which complicated Cellular utomata are concentrated on recently 50 rule extraction process. years and has become applicable in many sciences. The basic idea of cellular automata is quite simple: each cell in discrete time-steps updating its states according to a transition rule which is globally and synchronously applied to each cell. The cell value is determined by the configuration of its neighbors that is specified in transition rule by iteration. The updated values of each cell will become the inputs for the next iteration %,0'. Two most applicable neighborhood definitions in cellular automata are: Moore and extended Moore %,1]. In Moor neighborhood, adjacent cells considers as neighbors in vertical, hori8ontal and diagonal directions. The extended Moor neighborhood in its simplest form considers one cell over the Moor neighbors. The proposed approach used extended Moor neighborhood. It simply handles joint and disjoint letters and keeps performance in a good level. 0ig.1 illustrates a central cell and its 2. 0ig.2. (aI Model 1 of 3Muhammad3 pattern tiling 0rom the Nabi Mosque of Ca8vin (bIModel 2 of 3Muhammad3 pattern tiling 0rom the neighborhoods. In some literatures the beginning letter of Ma'soumeh shrine of Cum. (cI Model , of 3Muhammad3 pattern tiling the name of directions used to refer neighbor cells %,2' 0rom the Ma'soumeh shrine of Cum %,,'. 0ig.1 shows this method of naming to refer to the cells in an easy understanding way. 0or instance, 3NE-3 0ig.2 shows architectural buildings contain three refers to the northeast east cell and 3NN--3 refers to the models of 3Muhammad3 pattern that we called them north north east east cell. 6ecause in calligraphy the space 3model 13, 3model 23 and 3model ,3 respectively. is either white and leaved blank or colored with the ink, There is a common part in three models. 0ig. , shows we use two state cells for cellular automata to illustrate a process for creating this common part. basic ideas in calligraphy and simplify the implementation. Thus each cell with value 1 is colored or alive and each cell with value 0 is white or dead. 0ig.,. process for creating the common part between , models of 3Muhammad3 pattern 0ig.1. the extended Moore neighborhood The rest process for creating model 1,2 and , of 3Muhammad3 pattern are illustrated in figures . to 6 respectively. 432 15I Ei.EEi.NEEi.NNEEi.NNEi.NNi 16I Ei. EEi. NNEEi. NNEi 11I Ei. EEi. NNEEi 12I Si. SEi. SEEi. NEEi. NNEEi 14I Si. SSi. SSEi. SSEEi. EEi. NEEi. NNEEi 0ig... The rest process for generating model 1 of 3Muhammad3 pattern 20I Ei. SEi. SSEi. SSEEi 21I Ei. EEi. SEEi. SSEEi 22I Ni. NEi. NEEi. EEi. SEEi 2,I Ni. NNi. NNEi. NNEEi. EEi. NEEi 2.I Ei. 7i.EEi. NEi. NNEi. NNi. N7i. NN7i 25I SS7i. SSi. EEi. NEEi. NNEEi. SEEi 0ig.5. The rest process for generating model 2 of 3Muhammad3 26I SS7i. SSi. SSEi. Ei pattern 21I SSi. SSEi. SSEEi. Ei. EEi 22I Si. SSi. SEi. SEEi. SSEEi. Ni. NEi. NEEi These rules are generating the pattern. In each time step, any true rules are acting and generating a part of pattern. Each rule describes some neighbors of a cell that are alive. 0or example, rule (2I is points to the south and 0ig.6. The rest process for generating model , of 3Muhammad3 the southwest neighbors. If the mentioned neighbors of pattern any cell are alive, those cells come in to alive cells in the next time step. Thus it is possible to provide a flexible algorithm for The first rule is conserving the generated pattern generating these models of 3Muhammad3 pattern. lso from previous steps. Clearly, this rule determines that if common part rules are reused in the models and can make C was equal to 1 in the previous step, then C should the algorithm shorter and simpler. In our extracted rules, i iJ1 remain 1 in the next step. Other rules are defined based on the 3i3 index demonstrate current state and the 3iJ13 index neighborhoods. If the neighbors mentioned in a rule are demonstrate the next state of a cell. The proposed method alive and the others are dead, then that rule is true. determines flexible rules to generate other patterns as 7e provide an algorithm for generating all , models well. 0or example the rules for generating the common of 3Muhammad3 pattern. In this algorithm the sign 3 ⊕ 3 part between , models are as follows: means exclusive or.
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