Search results for: tiling

Authors: Seyyedeh Faezeh Miralami, Sahar Sayyadchapari, Mona Laleh, Zahra Poursafar

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Tiling patterns are magnificent display of decoration in Islamic period. They transform the dusty and dreary facades to splendid and ornate ones. Due to ideological factors and elements of Azari style decorations, geometrical patterns and vegetative designs became prevalent and pervasive in religious sites like mosques. Objectives: The objective of this research is a study of tiling patterns in Tabriz Kaboud mosque, as a splendid work of architecture in Azari style. In this study, the geometrical designs and tiling patterns employed in the mosque decorations are examined and analyzed. Method: The research is based on a descriptive analysis method. Data and information are collected based on documents library and field study. Then, polished and brushed, the study resulted in an illustrative conclusion. Findings: In religious sites such as mosques, geometry represents ‘divination’ in Christian theology and ‘Unity with God’ or ‘Tawhid’ in Islamic terminology. In other words, science, literature, architecture, and all forms of human expression and representation are pointed towards one cause, unity or divination. Tiling patterns of Kaboud Mosque, mostly hexagonal, circular, square and triangle, form outstanding architectonic features which recount a story, a narration of divination or unification with the One.

Keywords: tiling, Azari style, Tabriz Kaboud Mosque, Islamic architecture

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Authors: Rima A. Ajlouni

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The discovery of quasi-periodic structures in material science is revealing an exciting new class of symmetries, which has never been explored before. Due to their unique structural and visual properties, these symmetries are drawing interest from many scientific and design disciplines. Especially, in art and architecture, these symmetries can provide a rich source of geometry for exploring new patterns, forms, systems, and structures. However, the structural systems of these complicated symmetries are still posing a perplexing challenge. While much of their local order has been explored, the global governing system is still unresolved. Understanding their unique global long-range order is essential to their generation and application. The recent discovery of dodecagonal quasi-periodic patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. Astonishingly, many centuries before its description in the modern science, ancient artists, by using the most primitive tools (a compass and a straight edge), were able to construct patterns with quasi-periodic formations. These ancient patterns can be found all over the ancient Islamic world, many of which exhibit formations with 5, 8, 10 and 12 quasi-periodic symmetries. Based on the examination of these historical patterns and derived from the generating principles of Islamic geometry, a global multi-level structural model is presented that is able to describe the global long-range order of dodecagonal quasi-periodic formations in Islamic Architecture. Furthermore, this method is used to construct new quasi-periodic tiling systems as well as generating their deflation and inflation rules. This method can be used as a general guiding principle for constructing infinite patches of dodecagon-based quasi-periodic formations, without the need for local strategies (tiling, matching, grid, substitution, etc.) or complicated mathematics; providing an easy tool for scientists, mathematicians, teachers, designers and artists, to generate and study a wide range of dodecagonal quasi-periodic formations.

Keywords: dodecagonal, Islamic architecture, long-range order, quasi-periodi

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Authors: A. S. Mousa, R. I. Rajab, A. A. Pinto

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An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the Cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated.

Keywords: game theory, Nash equilibrium, envy Nash behavior, geometric tilings, bifurcation thresholds

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Authors: Wai Ho Darrell Kwok

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Building entities are valuable assets of a society, however, all of them are suffered from the ravages of weather and time. Facilitating onerous maintenance activities is the only way to either maintain or enhance the value and contemporary standard of the premises. By the way, maintenance budget is always bounded by the corresponding threshold limit. In order to optimize the limited resources allocation in carrying out maintenance, there is a substantial need to prioritize maintenance work. This paper reveals the application of Fuzzy AHP in a Facilities Management Company determining the maintenance priorities on the basis of predetermined criteria, viz., Building Status (BS), Effects on Fabrics (EF), Effects on Sustainability (ES), Effects on Users (EU), Importance of Usage (IU) and Physical Condition (PC) in dealing with categorized 8 predominant building components maintenance aspects for building premises. From the case study, it is found that ‘building exterior repainting or re-tiling’, ‘spalling concrete repair works among exterior area’ and ‘lobby renovation’ are the top three maintenance priorities from facilities manager and maintenance expertise personnel. Through the application of the Fuzzy AHP for maintenance priorities decision algorithm, a more systemic and easier comparing scalar linearity factors being explored even in considering other multiple criteria decision scenarios of building maintenance issue.

Keywords: building maintenance, fuzzy AHP, maintenance priority, multi-criteria decision making

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Authors: Vinodd Nayak

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10th & 12th are the most crucial period in a student’s life. It is the time when he or she has to make vital career choices and get the relevant professional education. Unfortunately most students are not aware of the multitudes of career options available to them. This leads to affect our social fabric of the society with issues like unemployment, stress etc. We have planned a guidance program for the youth in Maharashtra state which has 4 components; creating awareness about different career options, proper guidance and motivation, counseling for parents, and information on financial aid for unemployed youth we are conducting skill development programs. Currently we are conducting programs under 4 categories Uneducated Youth: Skill Development programs for unemployed youth in construction field (Carpentry/Masoning/Wlder/Electrician/Tiling etc..) in association with L&T Construction Training Institute Educated Youth: Il&FS: Training and Job Placement in the field of Finance and Customer Service NIS Sparta: Training and Job Placement in the field of Sales and Marketing Apeejay Inst. of Hotel Management: Training and Job Placement in the field of hospitality industry Skill India: Training and Job Placement in the field of IT Results: The results were really overwhelming. We were able to cater to approx. 10,000 students a year and the list is growing. Earlier we were only catering to schools and colleges, now we have started receiving invitations from other community organizations to conduct such programs for their communities Implications for Social Work and Social Development practice: It is a high time that Social work organisations need to get into such work as this will enhance people to improve their financial condition. We always believed that it is better to teach a man to fish than feed him.

Keywords: youth education, career guidance, skill development, parental guidance

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Authors: Catarina Cruz, Ana Breda

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Tiling problems have been capturing the attention of many mathematicians due to their real-life applications. In this study, we deal with tilings of Zⁿ by Lee spheres, where n is a positive integer number, being these tilings related with error correcting codes on the transmission of information over a noisy channel. We focus our attention on the question ‘for what values of n and r does the n-dimensional Lee sphere of radius r tile Zⁿ?’. It seems that the n-dimensional Lee sphere of radius r does not tile Zⁿ for n ≥ 3 and r ≥ 2. Here, we prove that is not possible to tile Z⁷ with Lee spheres of radius 2 presenting a proof based on a combinatorial method and faithful to the geometric idea of the problem. The non-existence of such tilings has been studied by several authors being considered the most difficult cases those in which the radius of the Lee spheres is equal to 2. The relation between these tilings and error correcting codes is established considering the center of a Lee sphere as a codeword and the other elements of the sphere as words which are decoded by the central codeword. When the Lee spheres of radius r centered at elements of a set M ⊂ Zⁿ tile Zⁿ, M is a perfect r-error correcting Lee code of word length n over Z, denoted by PL(n, r). Our strategy to prove the non-existence of PL(7, 2) codes are based on the assumption of the existence of such code M. Without loss of generality, we suppose that O ∈ M, where O = (0, ..., 0). In this sense and taking into account that we are dealing with Lee spheres of radius 2, O covers all words which are distant two or fewer units from it. By the definition of PL(7, 2) code, each word which is distant three units from O must be covered by a unique codeword of M. These words have to be covered by codewords which dist five units from O. We prove the non-existence of PL(7, 2) codes showing that it is not possible to cover all the referred words without superposition of Lee spheres whose centers are distant five units from O, contradicting the definition of PL(7, 2) code. We achieve this contradiction by combining the cardinality of particular subsets of codewords which are distant five units from O. There exists an extensive literature on codes in the Lee metric. Here, we present a new approach to prove the non-existence of PL(7, 2) codes.

Keywords: Golomb-Welch conjecture, Lee metric, perfect Lee codes, tilings

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Authors: Yuxi Liu, Boris Belousov, Mehrzad Esmaeili Charkhab, Oliver Tessmann

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This paper presents a computational solution for designing reconfigurable interlocking structures that are fully assembled with SL Blocks. Formed by S-shaped and L-shaped tetracubes, SL Block is a specific type of interlocking puzzle. Analogous to molecular self-assembly, the aggregation of SL blocks will build a reversible hierarchical and discrete system where a single module can be numerously replicated to compose semi-interlocking components that further align, wrap, and braid around each other to form complex high-order aggregations. These aggregations can be disassembled and reassembled, responding dynamically to design inputs and changes with a unique capacity for reconfiguration. To use these aggregations as architectural structures, we developed computational tools that automate the configuration of SL blocks based on architectural design objectives. There are three critical phases in our work. First, we revisit the hierarchy of the SL block system and devise a top-down-type design strategy. From this, we propose two key questions: 1) How to translate 3D polyominoes into SL block assembly? 2) How to decompose the desired voxelized shapes into a set of 3D polyominoes with interlocking joints? These two questions can be considered the Hamiltonian path problem and the 3D polyomino tiling problem. Then, we derive our solution to each of them based on two methods. The first method is to construct the optimal closed path from an undirected graph built from the voxelized shape and translate the node sequence of the resulting path into the assembly sequence of SL blocks. The second approach describes interlocking relationships of 3D polyominoes as a joint connection graph. Lastly, we formulate the desired shapes and leverage our methods to achieve their reconfiguration within different levels. We show that our computational strategy will facilitate the efficient design of hierarchical interlocking structures with a self-replicating geometric module.

Keywords: computational design, SL-blocks, 3D polyomino puzzle, combinatorial problem

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Authors: Carla Aramouny

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Digital fabrication, between advancements in software and machinery, is pushing practice today towards more complexity in design, allowing for unparalleled explorations. It is giving designers the immediate capacity to apply their imagined objects into physical results. Yet at no time have questions of material knowledge become more relevant and crucial, as technological advancements approach a radical re-invention of the design process. As more and more designers look towards tactile crafts for material know-how, an interest in natural behaviors has also emerged trying to embed intelligence from nature into the designed objects. Concerned with enhancing their immediate environment, designers today are pushing the boundaries of design by bringing in natural systems, materiality, and advanced fabrication as essential processes to produce active designs. New Territories, a yearly architecture and design course on digital design and materiality, allows students to explore processes of digital fabrication in intersection with natural systems and hands-on experiments. This paper will highlight the importance of learning from nature and from physical materiality in a digital design process, and how the simultaneous move between the digital and physical realms has become an essential design method. It will detail the work done over the course of three years, on themes of natural systems, crafts, concrete plasticity, and active composite materials. The aim throughout the course is to explore the design of products and active systems, be it modular facades, intelligent cladding, or adaptable seating, by embedding current digital technologies with an understanding of natural systems and a physical know-how of material behavior. From this aim, three main themes of inquiry have emerged through the varied explorations across the three years, each one approaching materiality and digital technologies through a different lens. The first theme involves crossing the study of naturals systems as precedents for intelligent formal assemblies with traditional crafts methods. The students worked on designing performative facade systems, starting from the study of relevant natural systems and a specific craft, and then using parametric modeling to develop their modular facades. The second theme looks at the cross of craft and digital technologies through form-finding techniques and elastic material properties, bringing in flexible formwork into the digital fabrication process. Students explored concrete plasticity and behaviors with natural references, as they worked on the design of an exterior seating installation using lightweight concrete composites and complex casting methods. The third theme brings in bio-composite material properties with additive fabrication and environmental concerns to create performative cladding systems. Students experimented in concrete composites materials, biomaterials and clay 3D printing to produce different cladding and tiling prototypes that actively enhance their immediate environment. This paper thus will detail the work process done by the students under these three themes of inquiry, describing their material experimentation, digital and analog design methodologies, and their final results. It aims to shed light on the persisting importance of material knowledge as it intersects with advanced digital fabrication and the significance of learning from natural systems and biological properties to embed an active performance in today’s design process.

Keywords: digital fabrication, design and craft, materiality, natural systems

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