Nowadays symmetrical patterns are widely used in various industries, such as jewelry design, carpet design, patterns on wallpaper, and textile design. During the design stage, designers perform most of the work manually. Therefore, the development of methods for symmetrical pattern generation is beneficial. In this paper, we are going to present some methods for generating symmetrical patterns using the discrete dynamical system. For this, the discrete dynamical system is considered as a standard iterative method, and then the general algorithm applied for Polynomiography is used for this to generate patterns. Through phase portrait, we analyze the conditions of the existence of some conventional symmetries. Several non-standard iterative methods can be employed to create a variety of visually appealing patterns. These methods include Mann iteration, Ishikawa iteration, and S-iteration which we use them. Through numerous examples, it is demonstrated that by manipulating the parameters and coefficients, it is possible to generate beautiful symmetrical patterns that have potential artistic applications.

Spurs are hydraulic structures used to protect riverbanks from erosion and to concentrate the flow on the river axis. As the flow approach the spurs, discontinuous in the streamlines are occurred and vortices form before the spurs. By placing the spurs in an open channel, scours occur before and after the spurs due to changes in flow conditions and velocities. Determination of velocity distributions around the spur accurately is extremely important for spur design. For a sustainable and hydraulically efficient spur design, flow velocities, flow conditions, sediment characteristics and stream morphology around the spur should be well investigated. In this study, the changing flow velocities and flow patterns on the upstream side of two spurs with were investigated. Two spur which have same geometry placed in an open channel system at an angle of 90o with the side wall. For 2 different discharge values (Q=17.66 lt/sn and Q=15.27 lt/sn), 3-Dimensional velocity measurements were made with ADV (Acoustic Doppler Velocimetry) at 20 different points on the upstream side of the spurs. Velocity values obtained from the experiments were compared with the numerical models and gave consistent results with the numerical models. With these obtained velocity profiles, flow patterns are investigated.

Although we have access to a number of critical editions of Attā r's works, there still remain some problematic and ambiguous points in his works that cannot be clarified merely based on the codicological details. To elucidate such matters, it is indispensable to analyze closely the different aspects of Attā r's style based on the authentic documents to discover the general patterns. In this study, we deal with some of the symmetrical patterns recurring throughout all the layers (from the verses to the whole work) of Attā r's original poems. These patterns are classified into four main groups including repetition, parallelism, congruency, and a particular recurrent structure. The study of these symmetrical patterns, combined with the other stylistic and codicological details, can help us with evaluating the authenticity of some of the confusing parts in Attā r's works.

Symmetry is an analytical tool, used in recognition of intercultural relations as well as artistic objects comparison. It was first appeared in archaeological research since 1900’ s by studying the patterns that were depicted on the potteries. Various cultures (different historical periods) have various symmetry tastes. Some kinds of cultural changes are reflected in changes in symmetry preferences and/or in the presence of a new type of symmetrical pattern. The purpose of this research is to study the transformation or continuity of culture in historical periods of Hittite civilization based on the symmetrical pattern. The present research, based on the study of the written sources and the study of sculpture and bas-reliefs of the Hittite civilization regarding the mathematical nature of the symmetrical pattern, shows that the first signs of the use of symmetry in the art of this civilization have been introduced during the Great Hittite kingdom. In this period, there were various kinds of translation, Bi-lateral, Reflection, and Rotation symmetries in motifs, which seem to be rendered consciously, non-random and with a specific purposes. The presence of a new type of symmetry pattern during the Neo-Hittite period is likely to be as the result of a change in environment or the settlement pattern.

ABSTRACT Despite a wide range of components and criteria affecting travel behavior presented through empirical research, the results of these studies are inconclusive, which could be due to the difference between these components and criteria in the study areas. Therefore, this research presented a method to determine which factors in different physical developments affect travel behavior due to the differences in various physical developments. The required information was collected through 271 questionnaires at the level of three neighborhoods of Monirieh, Koye Bimeh, and Koye Golestan in Tehran, Iran, as the old, conventional, and new neighborhoods, respectively. ANOVA test was exerted to analyze the significant difference between different development patterns in three neighborhoods. Dunnett's T3 was applied to determine which neighborhood caused the difference between groups. Also, the factors affecting travel behavior were obtained based on exploratory factor analysis indicators. Finally, by comparing the results of the ANOVA test and regression analysis, it was discovered that factors such as car ownership, dependence and pro-liking for private cars, density and access to educational centers and parks, access to medical and service centers, and variety and density of retail stores had been introduced as the factors affecting travel behavior due to the differences in development patterns. However, proximity to the public transportation station, accessibility preferences in choosing a residence, dependence, and pro-liking for other than a private car, having a license, number of children under five years old, and age have influenced travel behavior regardless of the variation between neighborhoods. Extended Abstract Introduction Finding factors affecting travel behavior has been one of the main concerns of transportation planners. However, in the last two decades, the importance of the influence of the features of the built environment, including land use, along with demographic-economic characteristics, travel behavior, and attitudes of people, has been raised by urban planners. Studies seek to find factors affecting travel behavior, especially land use characteristics. Despite presenting a wide range of components and criteria affecting travel behavior, the results of the studies are inconclusive, which could be due to the difference between these components and criteria in the study areas. Therefore, this research presented a method to determine which factors in different physical developments affect travel behavior due to the differences in various physical developments. In order to do this, it must first be determined whether the study areas/different development patterns have a significant difference in terms of travel behavior or not. In case of a positive answer to the previous question, the following question is which study areas caused this difference. The next question arises: -Which physical and non-physical characteristics affect travel behavior due to distinctions between different development patterns?   Methodology The present research method is analytical and experimental based on quantitative methods. This research chose the frequency of travel by private car, public transportation, and walking as the travel behavior. According to the research's purpose, indicators and criteria affecting travel behavior were extracted after reviewing the theoretical and experimental literature. Then, the required information was collected through 271 questionnaires at the level of three neighborhoods of Monirieh, Koye Bimeh, and Koye Golestan as the old, conventional, and new neighborhoods, respectively. The questionnaire was compiled as a Likert scale in five parts of travel information, demographic-economic characteristics, perceptual characteristics of land use, travel habits, and access preferences of people in choosing their residence. ANOVA test was used to analyze the significant difference between different groups of a characteristic (here, different development patterns or the three case studies). Dunnett T3 was exerted to determine which neighborhood caused the difference between groups. Also, the factors affecting travel behavior were obtained based on exploratory factor analysis indicators. Finally, by comparing the results of the ANOVA test and regression analysis, it was discovered which factors affecting travel behavior were due to the differences in study areas and which factors affect travel behavior regardless of development patterns.   Results and discussion This research aims to identify the factors affecting travel behavior due to the differences in development patterns. In this regard, the findings in line with the first research question show that the frequency of three modes of travel, by private car, transportation, and pedestrian, differ significantly in the three neighborhoods. Furthermore, ANOVA test results depict that there is a significant difference between these three neighborhoods in terms of factors affecting travel behavior, such as perceptually environmental characteristics of the neighborhood, dependence and pro-liking for personal cars, variety and density of retail stores, density and access to educational units and parks, access to medical and service centers, and car ownership. Finally, by comparing the results of the ANOVA test with the regression analysis assessing the relationship between physical and non-physical factors (the same indicators in the same study areas) with travel behavior, the factors affecting travel behavior owing to different development patterns were identified. Factors such as car ownership, dependence and pro-liking for private cars, density and access to educational units and parks, access to medical and service centers, and variety and density of retail stores have been introduced as the factors affecting travel behavior due to the differences in development patterns. However, proximity to the public transportation station, accessibility preferences in choosing a place of residence, dependence, and pro-liking for other than a private car, having a certificate, number of children under five years old, and age have influenced on travel behavior regardless of the variation between neighborhoods (different physical development patterns).   Conclusion In In order to discover the factors affecting travel behavior due to the differences in patterns of physical development, this research has provided a more detailed analysis of the factors affecting travel behavior. It has achieved more accurate components than previous studies in this regard. Detailed analysis of studies related to travel behavior and finding the main components affecting it, considering the extent of variables and data, can pave the way for professionals in transportation planning and urban planning, in addition to providing detailed methods and criteria in the related literature.   Funding There is no funding support.   Authors’ Contribution Authors contributed equally to the conceptualization and writing of the article. All of the authors approved thecontent of the manuscript and agreed on all aspects of the work declaration of competing interest none.   Conflict of Interest Authors declared no conflict of interest.   Acknowledgments  We are grateful to all the scientific consultants of this paper.

Man is by nature a lover of beauty, and the feeling of enjoying the beauty of anything or a person is the result of understanding the order and harmony in it. In aesthetic discussions, to beautify a work or phenomenon, various factors such as symmetry, balance, periodicity, proportionality, repetition, contradiction, etc. can be considered. Symmetry, as one of the most fundamental foundations of art and beauty in understanding the order between the components, plays an undeniable role in most sciences and arts. Among them, we can mention sciences and arts such as mathematics, geometry, astronomy, architecture, music, painting, carpet weaving, design, gilding, woodcarving, literature, etc. From the studies of this research, it appears that there are many similarities and differences between the two Islamic-Iranian arts of literature and architecture in terms of words and concepts. Sometimes literature uses architectural designs and patterns in creating imaginary images, and sometimes architecture uses the words and concepts of literature in creating some designs and designs of buildings and even calligraphy. .In this research, with the help of library tools and document research and data analysis, after mentioning some commonalities of Persian literature and architecture, we have studied the manifestation of literary concepts in the symmetrical patterns of the dome of Sheikh Lotf-Allah Mosque in Isfahan.

The art and techniques of colorful tiling in domes, inscriptions, minarets of mosques, buildings and historical monuments from antiquity, is a valuable and important document about the decorations of ancient Iranian architecture. Ancient mathematicians, designers, and practitioners used the geometric methods of knot arrangement, Yazdi-bandi, Muqarnas, (Ahu pai) and other methods, with the help of geometric arrangement of squares, diagonals, rhombuses, and techniques such as "square-to-circle correlation" with the term "mandala. The identification and production of the primary units of geometrical "motifs" began centuries ago and includes geometric units in two dimensions. These motifs have been developed in different historical periods by geometers and designers. It is clear that mathematical-geometric laws have remained fixed in motifs throughout the past. This means that the laws of symmetry have a main origin, in a way that they have been fixed in different historical periods. On the other hand, alignment, balance and symmetry are necessary for each other. Geometry has been used since ancient times to measure the surfaces of buildings and agricultural lands. Points, line segments, angles, circles, squares and triangles have been used in the production of two-dimensional patterns in the order of regular patterns.

Abstract: Different cultures have various patterns for painting their decorative surfaces. Thus, preference for the use of various patterns is different in cultures, and these preferences are changed based on cultural relations or changing social substructures. This is the summary of symmetrical patterns theory in cultures that were tested by anthropologists and archaeologists for many years. Thus, symmetry has emerged as a powerful platform to understand the similarities and cultural differences between communities. It is believed that symmetry for a culture can be inherited like the human genes that are inherited from parents like the traits such as height and diseases; Cultural characteristics through symmetry can be transmitted to the next generation. But what is important to us is that so far researchers have not paid attention to the role of human cognition and cognitive activation in these interactions and preferences. In the paper, while studying the origin of the symmetrical patterns of complicated Dalma culture and associated cultural relations, we are looking for a cognitive factor that affects the stability or change of symmetrical patterns. The results show that the mirror neurons structure of an individual plays a vital role in preference for the use of a symmetrical pattern such that during cultural contacts, with the firing of mirror neurons, common patterns in a cultural tradition is imitated and prioritized. It means that unconsciously people show a preference for using such unfamiliar patterns. Accordingly, cultural contacts more possibility was as a result of trading, especially obsidian trading. Thus, such trading simultaneously with the Dalma cultural Period led to contact between northwestern Iran and its cultural horizon in the southern Caucasus, eastern Anatolia, and northern Mesopotamia. As a result of such connections, we witness the spread of the symmetrical pattern of the half pottery in the interior regions of modern Iran. IntroductionSymmetry means dividing a shape or object into two equal parts so that the two sides are the same in every respect. However, symmetry is not limited to this definition. The motor behavior and regular repetition of a motif on the surface, regardless of its shape and type, is part of the concept of symmetry, which has entered studies related to culture to a new stage (Faizi & Vahdati Nasab, 1394). Symmetry is divided through mathematics into 1, 2, and 3 dimensions, while it, as biological and cognitive characteristics of human societies, has left a significant footprint. Anthropologically, symmetry is an important perceptual indicator that has evolved to understand a form and is closely related to the visual function of the brain (Hodgson, 2009). However, the patterns of symmetry created on the surface are the result of the cognitive activities of Homo sapiens sapiens (Wynn, 2002) On the other hand, there are neurons called mirror neurons in the human and ape brains that fire when a person is performing or watching action(Rizzolatti, 2005). These patterns makes the study of symmetry valuable in the analysis of culture and cultural interactions (Brainerd, 1942). From a pattern recognition point of view, archaeologists believe that the early use of symmetry varied in different cultures. It means that the patterns were exchanged between cultures through cultural contact unconsciously, and therefore their chronology is likely (Hann 2003a-c; Washburn & crow1998, 2004, crow 1998; Washburn, 1999). But despite its importance, up to now, little attention has been paid to symmetry in the archaeology of Iran and its nature remains unclear. The principal question of the present study is about cognitive and cerebral factors affecting the prioritization of different symmetries in different cultures. Assuming that human cognitive ability is the principal factor concerning the environment and creating the culture and cultural relationships, we seek to recognize these vital factors in these priorities. In this article, to present the cognitive model of the priority of using symmetry in each culture, while studying the symmetric mathematical model of the Dalma culture and its symmetrical relationship with neighboring cultures, the vision and cognitive principles of symmetry have been studied. It is necessary to explain that the reason for choosing Dalma culture is the complexity of chronology, the possible time gap between the Chalcolithic and the Hajji Firuz Neolithic culture, and insufficient knowledge of the Northwestern cultures in this period.Dalma Tepe is located in the province of West Azerbaijan in the southwest of Lake Urmia. From layers 4 and 5 of this site, a remarkable collection of pottery has been obtained, which is different from the pottery of the previous period. These pottery are dated after the late Neolithic, Hajji Firuz, and the Middle chalcolithic, Pizdeli, in the Northwest. They are distributed in the first half of the fifth millennium and the second half of the fifth millennium in the Central Zagros. They are common pottery of the early chalcolithic and Middle Neolithic period (Abedi et al., 2015). Therefore, Dalma pottery is identified in the Northwest chronology with a time gap after Hajji Firuz and chronologically coincides with Obaid 3 in Mesopotamia (Rahimi Sorkhani & Eslami, 2018). In recent excavations in the region, this time gap has been filled, and Dava Göz Khoy1 has been identified as a transition period to Chalcolithic (Abedi et al., 2018). Contrary to Solecki’s opinion (1973), we believe that Dalma painted is not the result of Hajji Firuz’s painted style. These sherds are similar only in terms of available materials in the environment, and in the Dalma period geometric patterns are more complex and more regular due to the use of different symmetry.  According to the theory of systems, we do not consider any culture closed. On the other hand, according to the interaction theory, Dalma culture forms a subset of symmetrical patterns of Halaf. The strategic position of Solduz valley due to obsidian trade was the cause of such an interaction and effect. Accordingly, we claim that human mirror neurons in the Neolithic and chalcolithic were fired for both designers and observers when drawing symmetrical bands or two-dimensional patterns. Through these neurons, they transferred the symmetry of other cultures to their own subconsciously. ConclusionUnconscious activation of mirror neurons while watching a symmetrical pattern causes the patterns to shift from one culture to another or prioritize that pattern. It is the function of mirror neurons that causes different cultures to have varied priorities for painting their decorative surfaces. However, the most important features of mirror neurons are the same important features that are transmitted to individuals and cultures in contact with a culture when they view a symmetrical band or overall pattern. These characteristics include the possibility of unknowingly rapidly imitating a process, interpersonal differences in the performance of actions, and the effect of the environment on the performance of individuals. Therefore, we consider mirror neurons to be the main factor of the non-random distribution of symmetry priorities in cultures. As in this case study, the symmetry pattern of the common pottery tradition (Halaf) is imitated by Dalma pottery makers unconsciously during the cultural contact for obsidian exchange, with the unconscious firing of their mirror while looking at the painted pottery of Halaf culture. Accordingly, these patterns are transmitted based on the activity of mirror neurons and have spread over a wide area of the Northwest and Southwest of Iran during cultural contact.

Background: Symmetrical peripheral gangrene is usually associated with underlying medical problems and it is seldom seen in pregnancy. Sepsis though common in a setting of delivery by unskilled midwife is rarely accompanied by symmetrical gangrene.Case Presentation: We report a case of symmetrical peripheral gangrene which occurred in the winter, triggered possibly by sepsis and a single dose of ergot. A high index of suspicion, early diagnosis and intervention with appropriate measures will result in favorable outcome in such cases.Conclusion: Although postpartum period is of high risk for sepsis and use of ergot alkaloids is common in labor but occurrence of peripheral symmetrical gangrene is rare. A high index of suspicion for the diagnosis and timely intervention will prevent irreparable damage and loss of limb.