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Takagi–Landsberg surface Fractal-Based Computational Modeling and Shape Transition of a Hyperbolic Paraboloid Shell Structure


Iasef Md Rian


Nexus Network Journal 20(2), 437-458, 2018


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. LINK

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


Iasef Md Rian, Mario Sassone & Shuichi Asayama


Computer-Aided Design 98, 40-53, 2018


This paper has applied the concept of fractal geometry in designing a grid-shell-like complex spatial structure. The property of the fractal dimension which characterizes the level of roughness of a shape has been particularly explored in this study for designing a complex-shaped spatial structure by taking a paraboloid as a basic shape of reference. A factor of fractal dimension which is known as the relative size value (w) plays the key role in changing the surface texture in accordance with the changing of fractal dimension. In this paper, the relative size value (w) has been specifically applied to study the texture-based shape morphogenesis of a paraboloid by using the reference of the Takagi–Landsberg’s fractal surface. This research is curious to see how this surface morphogenesis impacts on the structural behavior and unveils an opportunity to develop a new kind of form. For this purpose, we have computationally generated a parametric model of a grid-shell-like structure by making a paraboloid as a basic geometric framework and by adding an extra supporting frame in order to avoid any structural failure during the surface morphogenesis of the outer profile. A structural comparison has been done in between the grid-shell-like structure having the paraboloid-based smooth outer profile and the structure having a fractal-based unsmooth outer profile. A real-scale physical prototype of a fractal-based grid-shell-like structure has been constructed to see its architectural appearance, real-world structural behavior, practical applicability and constructability. LINK

Computational Design of a nature-inspired architectural structure using the concepts of self-similar and random fractals


Iasef Md Rian & Shuichi Asayama


Automation in Construction 66, 43-58, 2016


This paper aims to explore the scope of applying the concept of fractal geometry in the field of architecture and construction. There are mainly two different types of fractals – self-similar fractal and random fractal. In this paper, both types of fractals are used to design a nature-inspired architectural structure with the strategy of exploring the potency of fractal geometry as a geometric framework that can offer new structural forms. Based on themathematical formulations of self-similar fractal shape and randomfractal shape, tree-inspired branching supports and natural terrain inspired unsmooth crinkled roof are modeled using the algorithms of Iterated Function System and Midpoint Displacement (Diamond Square Algorithm) method respectively. Fractal dimensions are calculated to assess the visual complexity of the roof surface and branching supports. Finite element analysis is performed to assess the structural strength of the model with respect to changing of fractal dimensions. LINK

Fractal-based generative design of structural trusses using Iterated Function System


Iasef Md Rian & Mario Sassone


International Journal of Space Structures 29 (4), 181-204, 2014


The purpose of this study is to apply the notion of fractal geometry in designing structural roof trusses. Fractal geometry, commonly characterized by the features of recursive self-similarity, is considered as a rule-based geometric system that can be generated by using the process of the Iterated Function System (IFS). Lattice configurations of conventional trusses generally show some extend of ‘self-similarity’ features that loosely and sometimes closely resemble with the properties of fractal shapes. The typical configurations of these regular trusses are strategically designed to provide adequate strength and stability to the structures for carrying enough vertical and wind loads. This paper, using the Iterated Function System based on Barnsely's contraction mapping as a generative design method, proposes a new family of truss designs that follow the concept of fractal geometry. The Hausdorff dimensions and the Box Counting dimensions are evaluated to measure the fractality and detailness of the lattices of proposed fractal-based trusses. It also briefly investigates their mechanical properties for analyzing their practical feasibility in construction. LINK

Tree-inspired dendriforms and fractal-like branching structures in architecture: A brief historical overview


Iasef Md Rian & Mario Sassone


Frontiers of Architectural Research 3 (3), 298-323, 2014


The shapes of trees are complex and fractal-like, and they have a set of physical, mechanical and biological functions. The relation between them always draws attention of human beings throughout history and, focusing on the relation between shape and structural strength, architects have designed a number of treelike structures, referred as dendriforms. The replication and adoption of the treelike patterns for constructing architectural structures have been varied in different time periods based on the existing and advanced knowledge and available technologies. This paper, by briefly discussing the biological functions and the mechanical properties of trees with regard to their shapes, overviews and investigates the chronological evolution and advancements of dendriform and arboreal structures in architecture referring to some important historical as well as contemporary examples. LINK

Pop-up technique of origamic architecture for post-disaster emergency shelters

Iasef Md Rian, Dongkuk Chang, Jin-Ho Park


Open House International 33 (1), 22-36, 2008

This paper presents a pop-up technique based on origamic architecture as a technological design solution for postdisaster temporary shelter systems. First of all, the concepts of disaster and post-disaster are briefly introduced, and the roles and needs of post-disaster temporary shelter systems, particularly in emergency periods, are reviewed. Second, pop-up techniques based on origamic architecture are briefly discussed. Third, a formal language for opening the cards of origamic architecture is introduced, out of which a geometric elasticity has been developed. With the language, a variety of flexible and expandable designs for shelter structures can be generated by incorporating different pop-up techniques. Finally, a prototype shelter has been constructed to demonstrate the adaptability and sustainability of the shelter within the local environment and the affected society, considering portability, low-cost, and easy in assembling by any unskilled person. LINK

Fractal geometry as the synthesis of Hindu cosmology in Kandariya Mahadev temple, Khajuraho

Iasef Md Rian, Jin-Ho Park,  Hyung Uk AhnaDongkuk Changb


Building & Environment 42 (12), 4093-4107, 2007

The underlying relationship between Hindu cosmology and fractal theory is manifested in Hindu temple where fractal geometry acts as the language. This paper has analyzed the Kandariya Mahadev temple at Khajuraho as the paradigm of Hindu temples with regard to fractal geometry and describes the syntheses of fractal features of the temple from the Hindu cosmology and philosophy. LINK

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