دانشگاه شاهد فصلنامه نگره 2676-7244 21 77 2026 04 01 Analyzing and Comparing the Hidden Geometry of Architecture with the Murals of Behnam House in Tabriz based on the Infrastructure Network تحلیل و تطبیق هندسۀ پنهان معماری با دیوارنگاری‌های خانۀ بهنام تبریز بر پایۀ شبکۀ زیرساختی 240 261 5031 10.22070/negareh.2024.18548.3314 FA احد نژاد ابراهیمی استاد گروه معماری، دانشکده معماری و شهرسازی، دانشگاه هنر اسلامی تبریز، تبریز، ایران 0000-0001-6025-1942 پریسا هاشم پور استاد گروه معماری، دانشکده معماری و شهرسازی، دانشگاه هنر اسلامی تبریز، تبریز، ایران. 0000-0000-0000-0000 سمیرا کریمی قلعه لر دانشجوی دکتری معماری، دانشکده معماری و شهرسازی، دانشگاه هنر اسلامی تبریز، تبریز، ایران. 0009-0008-2285-2171 Journal Article 2025 06 01 Introduction: Geometry was one of the integral principles of Iranian-Islamic architecture, which created the necessary harmony in different parts of a building with the help of proportions and Peymun. The use of a mesh background was one of the oldest manifestations of the presence of geometry in architecture, which was used as a guide for the architect to ensure proportions and basic harmony in the building. But geometry was not only specific to the art of architecture; geometry has also been used by artists in other Iranian-Islamic arts in a hidden form. By conducting various studies, researchers have come to the conclusion that geometry has been important not only in architecture, but also in other Iranian-Islamic arts such as miniature painting, and painters have used geometry for aesthetic purposes. Mural painting is one of the branches of the art of painting that has been used as decoration in Iranian historical buildings. Researchers believe that in Iranian-Islamic architecture, geometry was not only used in the main structure and spatial organization of buildings, but architects and artists also used this geometry in details such as decorations and motifs. Hidden geometry was a geometric coordinate system based on which the artist composed their work, and its purpose was to create a coherent whole. This coherent whole in architecture included plans, sections, details, and architectural decorations. Reticulated substructures found in scrolls such as the Topkapi Scroll were some of the most important documents to prove the use of hidden geometry by traditional architects in the construction of their buildings. These scrolls, which included plans and patterns of decorations aligned with reticulated substructure networks, indicated the coherence between building components. Therefore, it can be said that if such a grid-based infrastructure was used in the design of Iranian buildings, it should be possible to adapt the existing buildings to such networks. To investigate this issue, the historic Behnam House, which has valuable murals, was selected for the case study. Purposes & Questions: The purpose of the present study is to investigate the hypothesis regarding the use of geometric micro-patterns and a reticulated grid to compose and place motifs in the murals of Behnam House, similar to pattern drawing in Iranian painting, and to find the relationship between this reticulated grid and the architecture of Behnam House. The research questions are as follows: What is the relationship between the architectural geometry and the geometry of the motifs in the mural paintings in historical Iranian-Islamic houses? and what is the relationship between the pattern and geometry of the walls and the plan of Behnam House in Tabriz, and its mural motifs? Methods: The research is qualitative, and the method of this research is analytical-comparative. The data collection method is library and documentary research, and images related to the murals have also been recorded in the field. The analysis part of the research, which includes the analysis of hidden geometry in plans, murals, and drawings, has been carried out with the help of software such as AutoCAD and Photoshop. Findings & Results: According to the studies and analyses, the results of the study indicated that the hidden geometry in the mural painting of the Tannabi room of Behnam House is related to its architecture, so that both correspond to a single grid, that is, the artist designed the mural painting using the infrastructure network modules of the room’s architecture on a smaller scale. The square infrastructure network with horizontal and vertical lines obtained from testing different divisions with proportions is completely consistent with the Behnam House plan. The secondary and tertiary grids with specific proportions, obtained from the primary grid, are also consistent with the mural motifs of the Behnam House. In addition to the 45-degree rotation of this grid (the method used in the Tabriz school of painting), a template design obtained for placing motifs, in which the shamsa in the wall painting has been developed with a square proportion and the important components of mural painting such as oval frames, flowers and vases, shamsa and half-shamsa and half triangles are placed in this pattern of divisions with a proper order. مقدمه: هندسه از اصول جدایی‌ناپذیر معماری ایرانی- اسلامی است که با بهره‌گیری از تناسبات و پیمون، هماهنگی را در اجزای بنا ایجاد می‌کند. پژوهشگران با انجام مطالعات مختلف به این نتیجه رسیده‌اند که هندسه نه‌تنها در معماری، بلکه در هنرهای ایرانی– اسلامی همچون نگارگری نیز موردتوجه بوده و نگارگران از آن برای ارتقای زیبایی آثارشان بهره برده‌اند. دیوارنگاری، به‌عنوان یکی از شاخه‌های هنر نگارگری، در تزئین بناهای تاریخی ایران کاربرد داشته است. پژوهشگران بر این باورند که در معماری ایرانی-اسلامی، هندسه هم در ساختار اصلی و فضاسازی بنا و هم در جزئیاتی چون تزئینات و نقوش، به‌کاررفته است. اهداف و سؤال‌ها: هدف پژوهش حاضر، بررسی فرضیۀ استفاده از ریزنقش‌های هندسی و شبکۀ شطرنجی زیرساختی برای ترکیب‌بندی و جایگیری نقوش در ترسیم دیوارنگاری‌های خانۀ بهنام، مشابه ترسیم نقش‌ها در نگارگری ایرانی و یافتن ارتباط این شبکه شطرنجی با معماری بنای خانۀ بهنام است. سؤال‌های پژوهش این است که در خانه‌های تاریخی ایرانی –اسلامی چه ارتباطی بین هندسۀ معماری و هندسۀ نقوش دیوارنگاری‌ها وجود دارد؟ و چه ارتباطی میان الگو و هندسۀ جداره‌ها و پلان طنبی خانۀ بهنام تبریز با نقوش دیوارنگاری‌های آن وجود دارد؟ روش‌ها: در این مطالعه موردی، خانۀ تاریخی بهنام با دیوارنگاری‌های ارزشمند انتخاب‌شده است. روش پژوهش، تحلیلی- تطبیقی و شیوۀ گردآوری اطلاعات، کتابخانه‌ای و میدانی است. یافته‌ها و نتایج: نتایج نشان می‌دهد که شبکۀ شطرنجی به‌کاررفته در دیوارنگاری‌ها با شبکۀ شطرنجی زیرساختی معماری بنا هماهنگ است و هندسه و تناسبات نمای جداره‌ها بر الگوی جایگیری نقوش در دیوارنگاری‌ها منطبق است.

https://negareh.shahed.ac.ir/article_5031_461f6b568f5c5bfc47273a449953ee86.pdf