Analysis of the application of fractal geometry in Iranian cultural symbols (Case study of Iranian municipal symbols)

In the last half century, the artist has created the most complex and creative art forms using new sciences, such as mathematics, geometry, technology and computers. Fractal is a new branch of mathematical and computer science that can be studied. This geometry has been discussed by many architects and mathematicians for many years and its application in architecture and artificial geometry has been questioned, violated or defended. In the art of different periods, different structures and forms and even different paintings can be seen in fractals. The fractal property of a symbolic composition is in the interesting sequence of details. This sequence is necessary to maintain the attractiveness of the design. Irregular sets provide a better representation of many natural phenomena than classical geometric shapes. Fractal geometry provides a general framework for studying such sets. In the discussion of fractals, complexity is inevitable, and fractals themselves arise from complexity altogether. Fractals are established as an art form among people, both in the form of computer graphics and as a model for explaining many physical, medical, geographical, etc. phenomena, although interest in fractals is possible without any mathematical or scientific background. It may exist in individuals, but understanding mathematics, which can be applied to a wide range of objects, will certainly arouse a deeper interest in the individual. The interdependence between art and mathematics has not been constant at different times and has changed precisely, symbolically and almost logically. Countless facts and events that are beyond human comprehension have forced him to invent systems of various signs to express thoughts and concepts that are difficult to understand and describe verbally. Design is a visual language that, like any other language, is a way of transmitting data and communicating, and changes over time in the expectation of efficient visual feedback at all times. Since graphic designers make great use of cultural themes and symbols in logo design, it is necessary to develop a coherent and logical solution to make a more informed choice in logo design.In the past, mathematics was more concerned with sets and functions in which classic calculation methods could be applied. Fractals are shapes that are not regular at all, unlike Euclidean geometric shapes and their degree of irregularity is the same on all scales. Badge is one of the main topics in graphic art . This study intends to investigate the role of fractals in Iranian cultural symbols of municipalities.here, This is the question:why fractal can be seen more in Iranian art and it seems that fractal geometry is used as one of the most important tools with a scientific basis and part of Iranian insight and culture in the direction of graphic art.The research method of this research is descriptive-analytical and the method of collecting information is based on library. Dedicated resources are mostly in the form of articles.Fractal has multi-component image capability.It can be divided into many pieces.Each piece is a copy of the whole image that can be used in many ways. For this reason, fractals have found many applications in science and art.