The Short Tiles Category (original) (raw)
Related papers
2022
This is my third paper submitted to the Bridges Conference. Unfortunately it was rejected, and the reasons given by the reviewers was perfectly valid. The case being that this topic is too big to fit into the page limitation of eight pages. This gives me an opportunity to tell the story as it was intended in the beginning, and then publish in another channel that allows more space. -------------------------- The subject is about pattern creation, using a technique that includes modular tiles within 5-fold patterns. The tiles have a motif that cross over each side and interacts with the motif in the adjacent tiles. What is new in this paper is that these crossings are not at mid-point. Previous papers focused on non-equilateral tiles, but all tiles had midpoint crossings. Here I introduce the first non-midpoint category, called the Flat category. The Flat category is the missing link between two types of historical patterns, the Starry and the Floral pattern types (terms coined by Castera). As Flat tiles link these two worlds together, they enable a broader spectrum of historical patterns to be tiled, and gives promise to new interesting pattern where the two different pattern types are more distinctly shown than in historical patterns.
Retrieving the Design Method of the Islamic Decagonal Girih Patterns
Peter J. Lu, et al, in their recent report in Science magazine, suggest that the decago-nal girih patterns on the Darb-i Imam shrine, Isfahan, Iran, 1453G, are quasi-periodic and were constructed by tessellation, using a set of five tile types, which they called girih tiles. They doubted the architectonic ability of the medieval designers and accordingly they devaluated both the processes and the outputs of their creativity. Contrary to what they have suggested, this paper shows the manual and swift technique to design and implement the decagonal patterns, based on drawing three types of overlapped but hidden grids of equal intervals (two of them are tilted on both sides by 72° and 36°), using only a T-square and two triangles: 18°/72° and 54°/36°. Besides, it shows a simple method that the students of the 1 st and 2 nd years of architecture can use in order to draw any decagonal pattern found in Egypt or other countries; as well as to create new patterns using repeated modular-units, and to retrieve the authentic motifs and visual-identity in new local architectures.
International Journal of Architectural Computing
This research challenges the long-standing paradigm that considers compositional analysis to be the key to researching historical Islamic geometric patterns. Adopting a mathematical description shows that the historical focus on existing forms has left the relevant structural similarities between historical Islamic geometric patterns understudied. The research focused on the hexagonal-based Islamic geometric patterns and found that historical designs correlate to each other beyond just the formal dimension and that deep, morphological connections exist in the structures of historical singularities. Using historical evidence, this article identifies these connections and presents a categorization system that groups designs together based on their “morphogenetic” characteristics.
Classifying Hexagonal Tilings in Islamic Architecture with a Single Numerical Parameter
Islamic designers drafted a large variety of hexagonal patterns in various media, including stone, tile, wood and cloth, throughout the medieval Islamic world. To highlight the geometric similarities among these patterns, we present a simple scheme to classify different types of hexagonal tilings in Islamic architecture, using a single numerical parameter. Islamic artisans and designers exploited geometry to create a wide variety of intricate patterns in a range of media, including brick, stone, ceramic tile, wood and cloth. In many cases, the underlying structure of these patterns was derived from compass and straightedge techniques [1]; on other cases, particularly decagonal and pentagonal geometry, a set of prototiles known as " girih tiles " was used to lay out geometric patterns [2]. One of the simplest periodic structures is based on tiling the plane with hexagons, forming a honeycomb lattice. In this paper, we illustrate how this simple hexagonal honeycomb structure was elaborated to form a range of line patterns that appear throughout Islamic art and architecture; these patterns are expressed in a number of different media: brick, stone, ceramic and cloth. Although these patterns may appear at first glance to be quite different, we show that in fact these patterns all share not only the same symmetry, but also the same underlying structure: hexagons placed at the vertices of a tessellation of hexagons of a different size. We present a number of patterns that can be classified in part by a single dimensionless numerical parameter: the ratio of the length of the hexagons that appear in the final pattern relative to that of the underlying honeycomb lattice, with only some minor variations. This simple scheme allows a large number of patterns to be compared with only a single number, facilitating comparison and contrast among this collection of historical Islamic art and architecture. The drafting of a hexagonal honeycomb grid using a compass and straightedge was well understood both by the ancient Greeks and by medieval Islamic architects and designers. The specific sequence of steps using the compass and straightedge to create the honeycomb tessellation of hexagons has been well illustrated in a number of publications [1, 3]. Line patterns with underlying hexagonal geometry have appeared throughout Islamic art and architecture. Perhaps the simplest way to decorate this grid is to place a motif at the vertex of each hexagon in the grid; one common motif is another hexagon, which appears in a large number of patterns throughout Islamic history. Examples are expressed in a wide variety of materials, including brick, stone, ceramic and cloth, and cover a range of dates and locations throughout the Islamic world, as shown in Fig. 1, where the underlying hexagonal honeycomb grid is delineated with black dotted lines, and the decorating hexagon motifs are marked in red.
Normalised grid/motif based patterns-Islamic geometric patterns
Proceedings. 1997 IEEE Conference on Information Visualization (Cat. No.97TB100165)
The studies of Isiamic Geometric Patterns (IGP) show that the methods of generation is based on a set of classical gridding systenzr. They are hierarchical and primarily based on the sacred geometrical primitives (triangle. square and circle). With such patterns, symmetries are as visible as the forms themselves. They signify an obtlous secondary meaning that is so often referred, in the sacred and religious texts, to as a higher order of significance. Based on the classical grid system, normalised grid-based patterns proposes a neu' language of design with a further aids of symmetries that holds these forms so robustly. It takes away their hierarchy by replacing it with a less tangible forms that are bounded by shear balance of symmetries. An underlined question for the reader is "Are we disturbing the semantics of these patterns, the meaning that ha1.e been portrayed by architect, tile designers anal visualists for a long time though their visual forms?"
Grid Method Classification of Islamic Geometric Patterns
Geometric Modeling: Techniques, Applications, Systems and Tools, 2004
This paper proposes a rational classification of Islamic Geometric Patterns (IGP) based on the Minimum Number of Grids (MNG) and Lowest Geometric Shape (LGS) used in the construction of the symmetric elements. The existing classification of repeating patterns by their symmetric groups is in many cases not appropriate or prudent [Joy97]. The symmetry group theories do not relate to the way of thinking of the artisans involved, and completely has ignored the attributes of the unit pattern and has focused exclusively on arrangement formats. The paper considers the current symmetric group theories only as arrangement patterns and not as classifications of IGP since they have a "global approach" and have failed to explore the possibilities in the construction elements of IGP. The Star, a central Rosette, which is the most important element of IGP, forms the core of our study. The paper proposes new nomenclature to be used in the description of the unit pattern based on the MNG and LGS used in the construction of a Star/Rosette pattern that can be used to achieve the final design. We describe and demonstrate procedures for constructing Star/Rosette unit patterns based on our proposed classification in a grid formation dictated by the final design of the unit pattern.
The Vocabulary of Perception and Design of Islamic Geometric Patterns
WIT Transactions on The Built Environment, 2018
This paper introduces a methodological distinction between three different scholarly interpretations of the forms and meanings of geometric ornaments in our heritage of Islamic art and architecture: an external cultural position, an esoteric religious argument, and an internal scientific approach. The major part of the paper is then directed beyond cultural allegiances or prescriptions of the Islamic faith and revolves instead around the internal formalistic and purely aesthetic aspects of reconstructing and making of geometric patterns, with the aim of exploring their vocabulary of perception, and their generative principles and inherent processes. The analysis starts at the very basic level where geometric patterns can be perceived as packing of open or enclosed surface polygons or linear configurations. Other means of perception relate to polygons' apparent and inherent geometry, tone or colour, and the application of a quasi-third dimension either through figure-ground reversal or by perceiving linear designs as interlocking elements beyond the 2d plane. The paper then investigates the relationship between means of visual perception and the inherent repetition, geometry and symmetry of patterns on the level of constituent polygons, repetitive tiles, and the design as a whole. Beyond the narrow meanings of likeness and identity in bilateral symmetry, alternative concepts of symmetry are introduced and then applied in setting up a comprehensive vocabulary of 2d geometric patterns based on the classification discovered by crystallographers and developed by mathematicians. The paper concludes by demonstrating the power of combining geometric and symmetry systems in recreating traditional designs or generating new patterns.
Evolution of Islamic geometric patterns
Frontiers of Architectural Research, 2013
This research demonstrates the suitability of applying Islamic geometrical patterns (IGPs) to architectural elements in terms of time scale accuracy and style matching. To this end, a detailed survey is conducted on the decorative patterns of 100 surviving buildings in the Muslim architectural world. The patterns are analyzed and chronologically organized to determine the earliest surviving examples of these adorable ornaments. The origins and radical artistic movements throughout the history of IGPs are identified. With consideration for regional impact, this study depicts the evolution of IGPs, from the early stages to the late 18th century.
Generating Islamic Quasi-Periodic Patterns
Journal on Computing and Cultural Heritage, 2018
The discovery of quasi-crystals has led to a great debate about their unusual structure. The big surprise is that these structures were found in Islamic art several centuries ago. This latest discovery drew the attention of scientists to propose several approaches for the comprehension of these structures by analyzing several quasi-periodic patterns spread around the Islamic world. In this article, we propose a systematic method for generating new quasi-periodic patterns inspired by existing Islamic historical patterns. The method builds Islamic quasi-periodic patterns based on a quasi-periodic tiling and a few intuitive parameters. Given a quasi-periodic tiling, the method divides its tiles (rhombs) into symmetric right triangles and constructs their template motifs. The construction of these template motifs is achieved by a systematic and well-organized process. The content of the tiles is obtained by applying mirror reflections to the constructed template motifs. Finally, the pat...