From fractal geometry to architecture: Designing a grid-shell-like structure using the Takagi–Landsberg surface

Rian, Iasef Md; Sassone, Mario; Asayama, Shuichi

doi:10.1016/j.cad.2018.01.004

Cited by 23 publications

(7 citation statements)

References 13 publications

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“…Self-organization in fractals (the functional system) and "Patkaneh": The law of self-organization in fractals creates the "hierarchy of connections" through nonlinear geometry properties of parabolas and hyperbolas, and the structure evolves and details into "geometric progressions". "In the law of selforganization, continuity, consistency, and rhythm are important characteristics in the hierarchy of connections created in the fractal structure" [21].…”

Section: Figure 11 the Process Of Dividing Bowls In Patkanehmentioning

confidence: 99%

Fractal Dimension of Islamic Architecture: The Structure of the "Patkaneh" in the dome of the Jame' Mosque of Ardestan, Iran

Ghouchani

MOKABERİAN

2022

Gazi University Journal of Science

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The Jame' Mosque of Ardestan is one of the famous buildings of the fifth century in Iran, which is known in the field of architectural studies of the Seljuk period, as a clear example of the architectural features of this period. However, this mosque has been neglected and no detailed studies have been conducted on it. What distinguishes this building as the subject of this research is the geometric shape of the transition area (ChapireSazi). This geometry presents a different structure compared to buildings of the same period. For this purpose, preliminary information was collected through direct field observations, interviews with masters of building restoration and library studies. Then, using a descriptive-analytical method, the construction of the dome structure of the Jame' Mosque of Ardestan has been investigated. The results show that in the ChapireSazi of this dome, a new method has been used to build a corner called "Patkaneh". This method is based on fractal geometry, which has similar and self-organized structures.

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Section: Figure 11 the Process Of Dividing Bowls In Patkanehmentioning

confidence: 99%

Fractal Dimension of Islamic Architecture: The Structure of the "Patkaneh" in the dome of the Jame' Mosque of Ardestan, Iran

Ghouchani

MOKABERİAN

2022

Gazi University Journal of Science

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“…As part of this statement, we return to the fact that the process of evolution of architecture in harsh climate conditions develops, at certain stages passing through points of bifuciation. And it is at these points of instability that the potential lies, demonstrating the options for further development, and the path is chosen, along which, in the end, evolution follows further [22][23][24].…”

Section: Use Of Fractal Structures In Polar Architecturementioning

confidence: 99%

Synergetic approach in the design of architectural systems for harsh climatic conditions

Khadieva

Novikov

2021

E3S Web Conf.

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Architecture is characterized by a correction of design approaches that take into account new discoveries. Changing scientific paradigm also influences this process by introducing extra details into the architectural objects workflows. The synergistic paradigm that influences mostly appears in the tendency to create architecture that meets the ideal standards of sustainable design, capable design which is of self-development and self-regulation. A unique feature of the synergistic paradigm that can fundamentally change the approach to design is its relation to the evolutionary process. According to this concept, evolution in its path passes through points of bifuciation – special states of instability – when possible ways of further development are clear and it becomes possible for us to choose and follow one of them. This approach takes into account changing data and corrects decisions during the process. This is especially relevant when designing architectural objects for harsh climate conditions, as additional difficulties may arise in the process of construction and operation, and the unexpectedly arising issues, which may unanticipated arise itself during the usage of the object and can have a disastrous effects on it.

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“…A crumpled paper, a non-integer-dimensional shape (D H ≈ 2.5) and an example of a random fractal, is stiffer than a two-dimensional flat paper (D H = 2.0) (Rian and Asayama 2016). There are also other built and unbuilt examples that show the structural potency and rationality of the fractal-like or fractal-based structures in architecture (Asayama and Mae 2004;Huylebrouck and Hammer 2006;Rian and Sassone 2014a, b;Rian and Asayama 2016;Rian et al 2018). These examples have motivated this paper's quest for finding unique and optimal forms of a spatial structure from the domain of non-integer dimensions using hypar as a benchmark example.…”

Section: Hypar Geometric Dimensions and The Fractal Possibilitymentioning

confidence: 99%

“…Reinforced concrete is also not difficult to caste on a prepared formwork; it is structurally monolithic and aesthetically expressive which can highlight the surface irregularity. Geometrically, the fractal-based hypar's Takagi-Landsberg surface is a rule-based complex form and it has a self-similar property which provides a hint of easy modular construction (Rian et al 2018). Each cross-section of the fractal-based hypar along the longitudinal direction is a Takagi-Landsberg curve, and each curve at a unit distance is the same, only their base heights are different (Fig.…”

Section: Constructability Of the Fractal-based Hyparmentioning

confidence: 99%

Fractal-Based Computational Modeling and Shape Transition of a Hyperbolic Paraboloid Shell Structure

Rian

2018

Nexus Netw J

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The concept of Takagi-Landsberg's fractal surface is applied in this paper for constructing a parametric model of a hyperbolic paraboloid (hypar) shell structure using the Midpoint Displacement Method (MDM) based on the Iterated Function System (IFS) and controlled by the relative size value (w), a factor of fractal dimension. This method of generating a parametric model of a hypar is applied to create a domain of non-integer dimensions through which the hypar surface passes through textural changes, thus transforming the smooth hypar surface from its two-dimensional shape to a higher but non-integer-dimensional irregular surface that results in the changes of structural behavior. This paper briefly compares the structural behavior between the regular hypar and the fractal-based irregular hypar, and also searches the optimal shape of the hypar in terms of minimum deformation from the collection of its regular version and its different levels of irregular versions.

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From fractal geometry to architecture: Designing a grid-shell-like structure using the Takagi–Landsberg surface

Cited by 23 publications

References 13 publications

Fractal Dimension of Islamic Architecture: The Structure of the "Patkaneh" in the dome of the Jame' Mosque of Ardestan, Iran

Fractal Dimension of Islamic Architecture: The Structure of the "Patkaneh" in the dome of the Jame' Mosque of Ardestan, Iran

Synergetic approach in the design of architectural systems for harsh climatic conditions

Fractal-Based Computational Modeling and Shape Transition of a Hyperbolic Paraboloid Shell Structure

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