Due to avoiding utilization of human figures and abstaining from idolatry, decorations have specific geometry in Islamic art and architecture. One of the striking characteristics of the knots (GIRIH) that has caused to dynamicity throughout its thousand-year history is its regeneration and diversification of the diverse geometric properties. GIRIH TILING decoration is part of geometric arts in the traditional buildings of the historic town of Masouleh dates back to eight hundred years. Traditional and local architects of this historical town have adopted special and intellectual plans for creating visual attractions in expression and creation of GIRIH TILING in the walls of the monuments. One of these valuable solutions is diverse geometric decorations patterns. Since the main facades of the houses in this town are directly located in the sunrise direction and it is accepted landscape for the citizens of this historical town, so the artists have shown their art and style in this part of the monument and built beautiful and harmonic diverse wooden windows and variety of these patterns are seen in all five neighborhoods in this town. GIRIH TILING consists of straight and broken lines on a regular basis that could be reasonably expanded in the surface. In the present study, it has been tried to classify the decorations in GIRIH TILING in the neighborhood of Masouleh and also investigate GIRIH TILING including scrolls and edges, and also the role of decoration in this element. The methodology of the research is based on field study and direct observation of the monuments and decorations and taking image and converting into Auto CAD files with dimensional analysis. Also, for description of GIRIH TILING, descriptive and library studies have been conducted. Questions that the research seeks to answer in this paper are: Can it 8 D be offered a defined pattern for opening GIRIH TILINGby analyzing of the decorations in neighborhood of Khanehbar in Masouleh? And also is the largest usage of the patterns seen in scrolls (middle or central plan)? Does scroll use most patterns in its margins? The GIRIH TILING patterns of “gavarehbari” with “boteh jegeh” designs (paisley), eight squares ornamental layout, rectangular, “hasht-chahr longeh tokhmedar”, and gavarehbari with the scales patterns are more common patterns. Fourteen patterns were seen in studying the GIRIH TILING patterns employed in the combined windows that “alat jafari chokhati” and then rectangular TILING and seven and eight sides TILING patterns were common. The patterns used in the friezes are mostly eight squares layouts. The most common patterns in the margins are four- side TILING in all parts. Diverse patterns of GIRIH TILING, besides with diverse combinations resulted from placing together and offering shapes in the friezes and marginal patterns have offered rich visual ornamentation in the historical city of Masouleh. Such studies aid reproduction of these patterns in the contemporary fine arts while preservation and documentation of the fine and visual patterns in the Iranian GIRIH TILING.

A TILING of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. In this paper some special polygonal TILING of sphere, nellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.

Decorations in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced to form intricate and complex patterns. Based on the shapes drawn from the circle, the earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all across the Islamic world. In 1086, 7 and 10 point GIRIH patterns (with heptagons, 5 and 6 pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10 point GIRIH became widespread in the Islamic world and this kind of GIRIH (10 point GIRIH) is the subject of this paper. GIRIH are elaborate interlacing patterns formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. GIRIH designs are traditionally made in different media including cut brickwork, stucco, and mosaic faience tilework. In architecture, GIRIH forms decorative interlaced strap work surfaces from the 15th century to the 20th century. Most designs are based on a partially hidden geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-, 4-, and 6 fold rotational symmetries which can fill the plane. The visible pattern superimposed on the grid is also geometric, with 10 and 12 pointed stars and a variety of convex polygons, joined by straps which typically seem to weave over and under each other. A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons. All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and thus suggest infinity. As it cited above, in this article, the method of 10 point GIRIH drawing is essayed and in order to maintain and ease the use of this lasting legacy in contemporary Iranian Islamic architecture, the question arises as to how to minimize the tools and stages of 10 point GIRIH drawing, invented a method for drawing schematics in addition to speeding up the practice of drawing and applying motifs. Authors, in response to this question, have developed a method called the baseline method (eighteen – eighteen Method), which presented an original pattern for drawing 10 point GIRIH motifs. The most difference between this new method and traditional method is that in this method, GIRIH would been drawn without using circle and compasses which results in a higher speed for GIRIH drawing. In this research, a combinative method has been used; the data collection is based on library documentation studies, and a kind of logical methodology based on mathematical relationships and mathematical proportions, is used for presenting a suitable model for drawing 10 point GIRIH.

Islamic art mostly avoids figurative images to avoid creating objects of worship. This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically-based decoration. Islamic patterns are created to lead the viewer to an understanding of the underlying reality, rather than being mere decorations, as writers interested only in pattern sometimes imply. In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul. These patterns in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6 to 13 point patterns by the 13th century, and finally to include also 14 and 16 point stars in the sixteenth century. So, many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate and complex patterns. In all of these patterns, circle has a very important role because the circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. Based on the shapes drawn from the circle, the earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all across the Islamic world. The next development, marking the middle stage of Islamic geometric pattern usage, was of 6 and 8 point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread. A wider variety of patterns were used from the 11th century. Abstract 6 and 8 point shapes appear in the Tower of Kharaqan at Qazvin, Persia in 1067, and the Al-Juyushi Mosque, Egypt in 1085, again becoming widespread from there, though 6 point patterns are rare in Turkey. In 1086, 7 and 10 point GIRIH (knot) patterns (with heptagons, 5 and 6 pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10 point GIRIH which became widespread in the Islamic world is the subject of this paper. GIRIHs are elaborate, interlacing patterns, formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. GIRIH designs are traditionally made in different media including cut brickwork, stucco, and mosaic faience tilework. In architecture, GIRIH forms decorative interlaced strap work surfaces from the 15th century to the 20th century. Most designs are based on a partially hidden geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-, 4-, and 6-fold rotational symmetries which can fill the plane. The visible pattern superimposed on the grid is also geometric, with 6, 8, 10 and 12 pointed stars and a variety of convex polygons, joined by straps which typically seem to weave over and under each other. A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons. All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and thus suggest infinity. As it is cited above, in this article, the method of 10 point GIRIH drawing is essayed and in order to maintain and ease the use of this lasting legacy in contemporary Iranian Islamic architecture, the question arises as to how to minimize the tools and stages of 10 point GIRIH drawing, invent a method for drawing schematics in addition to speeding up the practice of drawing and applying the motifs. Authors, in response to this question, focusing on one type of GIRIH (acute and obtuse 10 point GIRIH), have developed a method called the Golden Star, which presented an original pattern for drawing shapes with a constant ratio in the resulting elements based on golden proportions and golden ratio. In this research, a combinative method has been used. The data collection is based on library research method and published documents, and a kind of logical methodology based on mathematical relationships and mathematical proportions is used for presenting a suitable model for drawing the 10 point GIRIH. Therefore, in this paper a new method for 10 point GIRIH drawing is presented.

Relative peace of country in the Safavid era under the centralized First Shah Abbas reign, led to construction works in big cities. According to recognition of Shia religion in this era, and as a result, existence of a need for educational facilities in order to promotion of this religion, school-building tradition was popularized in this era more than other eras. In this regard, many schools were established by scholars, elders and rulers in the cities. Gradually, impressive attention was paid to architectural decoration in both inner and outer spaces of schools. TILING, brick work, Ma’ qeli and Karbandi decorations, and etc. are among decorations existed in Iranian schools. Usage extent of the mentioned decorations has been different in different eras. Khan School in Shiraz is one of the most important schools constructed by the rulers of Shiraz, Allah-verdi khan and his son Emam-Qoli Khan in this era. This school possesses a unique luster with four-porch pattern, chambers in two floors, a long gate, and various decorations such as Mogharnas, mosaic and seven-colored TILING with distinguished motifs and colors. This building is significant enough that has been mentioned in almost all of historical references and tourists’ travelogues in different eras. This school is significant from the architecture and architectural decoration, especially TILING points of view; and according to professor Pirnia, it is one of the most perfect schools in Iran from the plan and architectural decorations point of view. One of the obvious characteristics in the TILING decoration of this building, is the existence of different motifs in various styles. In addition, TILING in this building has a quite different color comparing with TILING in Safavid era buildings. The other point is the impressive similarity of its converge ceiling TILING with dome ceiling TILING of Sheikh-Lotf-o-Allah mosque in Isfahan. According to the construction date of the building and variety in its motifs and colors used in TILING decoration, the following question will arise; “ are these decorations related to Safavid era? Or they have joined the building during subsequent eras? Likewise, with which buildings do the motifs characteristics existed in TILING decoration of this building match? The main purpose of this study is, introduction, classification and checking the motifs existed in TILING decoration of Khan School of Shiraz. The approach of study is descriptive, comparative and data collection has been performed through field study and library method. According to occurrence of several civil wars, earthquakes, gradual erosion of the building and nonconformity of correct repair principles, architectural decorations and even the building plan have been basically changed. Obtained results suggest that most content of architectural decorations in Khan School of Shiraz includes Qajar and contemporary seven-colored tiles with herbal, bestial, geometric motifs and Quranic inscriptions in hot colors which have gradually replaced the decorations of Safavid era. Remained decorations from Safavid era have been affected by important buildings such as: Sheikh-Lotf-o-Allah mosque and Imam mosque in Isfahan due to the construction concurrency with these significant buildings.

This study has conducted on developing an innovative approach for the parametric analysis of daylighting and visual comfort through a sun responsive shading system as well as proposed a parametric pattern of Iranian Traditional GIRIH Tile (ITGT). On this basis, using parametric methods, the authors could change the parameters of a pattern to build modern geometric patterns and a bridge between traditional architecture approaches and modern technologies. The model was simulated in the Rhinoceros 3D as well as the Grasshopper, Honeybee, and Ladybug plugins were performed in order to evaluate daylighting and visual comfort performance. The objectives are estimating the annual daylight metrics and glare discomfort during four months from spring to summer when 3 variables (opening and getting closed, mass to space ratio, and time hours) that affect incoming daylight and visual comfort performance in a room. The results showed that the proposed model could significantly improve the shading flexibility to control daylight metrics and glare, through a full potential adaptive pattern to achieve the maximum visual comfort.

Geometric designs (both normal and abnormal) and purely geometric interlaced patterns involve mental imaginary forms which are essentially superior to the perception- based naturalistic images. The patterns were not aimed to capture the reality perceived through the eyes, but they were supposed to create a glimpse of astonishing beauty in the artist’s creative mind or soul. Due to avoiding utilization of human figures and abstaining from idolatry, decorations have specific geometry in Islamic art and architecture. One of the striking characteristics of the knots (GIRIH) that has caused to dynamicity throughout its thousand-year history is its regeneration and diversification of the diverse geometric properties. GIRIH tiles are used in Islamic art and architecture. Iranian Chinese Knotting is one of is one of traditional fields and professions that depends on geometrical patterns and on the first encounter, the spectator, is subconsciously affected by its discipline. Geometrical patterns, which are the source for the art Chinese Knotting, usually contain a polygon star inthe middle (the Shamseh) and some other geometrical figures so that they can cover the remaining space. Chinese knotting is not specifically a certain decoration or a means of conveying the emotions of the artist, but also the point of making them regarding to two ways: acting on the basis of their own knowledge and guiding others towards this knowledge. When a spectator looks upon the works of Chinese Knotting, they’re first affected by its beauty and especially its discipline, but after some more contemplation they are driven into the art’s mystical meanings. GIRIH tile is a part of Islamic architecture and art while its different types are used in the following arts: Wood carving, TILING, plaster, Khātam, brick work, mirror work, stone work and in carpentry as fences, door and window, wooden decorations and wood carving of Minbar and in blacksmith Iranian architecture. GIRIH tile is an intelligent interaction of aesthetics and function. Islamic artists have applied local materials in accordance to the functional requirements and cultural issues of each region. The valuable examples of this art are observed in historical city of Masoule located in the mountainous area of Masoule in Gilan (Iran). Wood is one of the highly applied materials in traditional architecture of Gilan with its different types. One of the greatest arts is seen in the historical city of Masoule with GIRIH tiles. Wood is used in this region due to its climatic condition and the need to a good thermal isolation against heat and cold weather. Also, wood is the first material being applied in openings. GIRIH tiles decorations in this historical city are abundant in the buildings while their main façade is to the south. One of the advantages of using GIRIH tiles in openings of this historical city is to control the direct light indifferent seasons of year. The aesthetic aspect is on the second priority. The beauty of GIRIH tiles, their coordination and part to total tendency in all openings have improved the unity and beauty of the historical buildings of Masoule. Sash window, other meshes and Telar with combination of decorative plants in the façade of buildings in Masoule have increased the aesthetics of this city. Historical city of Masoule is a good model for sustainable architecture and its final aim is respecting the culture and friendly relationship with nature and improving the life style of its residents. In the current study, the effort was concentrated on categorizing the designs (Chinese Knotting) used in the neighborhood of upper Kash-e Sar in Masouleh. The factors that affect the designs have also been inspected. The results show that 13 types of Chinese Knotting exist and that the most used pattern in this decorations is the pattern of eight-and-four. These results also show that the four fundamental parts of Chinese Knotting of Masouleh have been modeled on cultural, religious and natural elements. The four common elements of the Chinese Knotting of Masouleh are as follows: The Shamseh (the sun), the eight leaved lotus (symbol of the circle of nature), Chalipa (the symbol of the four main elements, existence) and the circe (symbol of eternity, although in this particular design it is the symbol of trees and nature). The methods of the study were a field-based and direct inspection of the structures. Also the inspection of the decorations (Chinese Knotting) was done using library research methods.

This paper describes an algorithm for TILING with polyminoes that consider rotation and/or reflection of figures in the steps of 90o. First, we review the previous parallel algorithms for TILING problems. Next, we propose a hybrid approach that is based on genetic algorithms (GA) and artificial neural networks (ANN). In this approach, the production of new members in GA and their evaluation are performed by a Hopfield neural network. Finally we compare our method with the previous works, and show that our method can produce global minima for many problems. The algorithm can be used for solving a variety of 2D-packing problems.

Qajar period can be seen as innovations and new developments in art and architecture. Among these developments, the growing relationship and exchanges with the West, Seeking new knowledge and new science to Iran, Special effects seen on the Art and Architecture and especially buildings decoration are in the Qajar period.Among the most important developments and New knowledge can be cited invention and log in photography, Log in and application of correspondence postal stamps and New European postcards.In this article, research methods is used description- Analysis and Studies Library in Architecture of The Masjid-Madreseh and also Field Studies To participate in the building and Direct observation. And the impact of these developments Review and assessment has been on the decorations Mashid-Madreseh of Qajar.Based on the reviews and studies, much of the decorating and TILING designs Mashid-Madrseh of Qajar is modeled Photos, stamps and postcards of that period.And images of monuments, Landscapes and architecture, Birds, grapes, crown, winged angels and humans, European men' s clothing, The flower vases and bowls and plates With various flowers, especially roses and lily In designs and decorative TILING And sculpted monuments seen.

Magnificent and beauty contributed to the architecture, especially during the Islamic era, is due to the decoration of the buildings. Chahar Bagh masjed-madreseh (mosque-school) in Isfahan is one of masterpieces of Safavid period and also masjed Seyyed is Isfahan is one of the buildings built in the early Qajar period, especially in terms of decoration and TILING patterns.Review, study and comparison of TILING patterns of the two buildings Can be recognized the cultural identity of these two buildings. The present research is based on the relative lack of scientific study of the historical architecture of the schools buildings in our country especially in the field of decorating and using analysis-description method and library studies in the field of architectural decorations of the two buildings and the field studies, tries to assist and compares the TILING patterns of the two distinctive buildings from Qajar and Safavid eras.Research findings show that the geometric and plant motifs on the tiles, decorating most of Chahar Bagh School, is abstract which benefits from a simple and fluent solidity, of which the decorative handwriting is dominantly Kufic and thulth handwritings. In masjed-madreseh Seyed, the decorative images such as fruits, grapes, flowers, vases, bowls, landscape and plates have been used in a high multiplicity and also applied, under the impact of decorative arts, in the West, as some realistic, abstract and non-duplication designs. Nastaliq hadwritiing is the most dominant in the inscriptions.