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Research Article

Computational form‑finding of a pavilion inspired by crystallization

Zahra Jalali1 · Mehrzad Esmaeili Charkhab1

Received: 16 December 2019 / Accepted: 17 April 2020 / Published online: 9 June 2020 © Springer Nature Switzerland AG 2020

AbstractDesigners and architects usually take inspiration from nature’s forms to develop their designs. Many of nature’s forms are highly sophisticated which only computational and algorithmic designs can be a solution. The purpose of this paper is to create a method and a tool for converting one of crystallization form-finding rules in nature into its use in the archi-tectural style with the digital design approach. For this purpose, the rules of crystallization are modeled geometrically through an algorithm in the visual programing language software. To illustrate the results of this research, a pavilion has been designed using the developed algorithm. In the process of transforming the rules of form-finding of a natural phenomenon into an algorithm, the gap might be too large that the form is no longer similar to the original idea. Nature-based algorithms are so complicated and converting them to mathematical algorithms causes inevitable changes in form-finding. In order to create algorithms inspired by nature, it is not necessary to exactly mimic form-finding in nature. Using this design method, the required function of the form may be affected, and its esthetics and shape will prevail. Therefore, there is a need for a balance between form, function and structure.

Keywords Form-finding · Algorithmic design · Generative design · Crystallization

1 Introduction

During recent years, architects transferred a variety of natural forms into their work alternated with strict geo-metrical shapes, based on their desired concept for design [1]. Designers usually take inspiration from nature’s forms to define a framework to use geometric systems that are inspired by complex or abstract forms of nature [2]. Because of impacts of technological functionalism, today’s esthetic views are focused more toward natural forms reflecting movement and flowing spaces [1].

Most of nature’s forms are complex and difficult to model using Euclidean, linear and other regular geometric systems [2]. Recently, computational tools have introduced innovative form-finding techniques that have revolution-ized architectural design. These techniques include gen-erative design, parametric design or algorithmic design [3].

The purpose of this research is to create a method for converting one of the form-finding rules in nature into its use in the architecture. To achieve this goal, a generative design has been developed.

There is a variety of generative form-finding techniques which still exist in architecture from long before the devel-opment of digital design [3]. The generative design seems to become a mainstream in architecture [4]. One of the main objectives of generative design in architecture is supporting human designers to use computational capa-bilities and automation in design process and design generation and also achieving efficiency, cost reduction, optimization, accuracy and consistency [5].

Architects now are enabled to explore numerous design possibilities using generative design. Although definition and implementation of generative design is debatable, architects have recognized its significance in design [4]. The use of computational design is a new paradigm and

* Zahra Jalali, zahrajalali@alumni.ut.ac.ir; Mehrzad Esmaeili Charkhab, mehrzad.esmaeili@ut.ac.ir | 1College of Fine Arts, University of Tehran, Tehran, Iran.

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is evolving by the support of mathematics. Creating new geometries in design may be the most prominent aspect of this gradual change, but the most radical change actu-ally emerged in new mathematical thinking [6].

One of the applications of digital tools is develop-ing complex forms that are difficult to be analyzed by a designer [7]. The proposed method in this research dis-cusses a specific natural algorithm for crystallization which results in a form regardless of function.

This paper continues with a comprehensive back-ground of the research in digital and generative designs. The method of converting crystallization rules into algo-rithms for architectural design is then explained. In the next step, process of a pavilion design through the devel-oped method as a case study is explained. The results along the generative design and an algorithm inspired by nature are finally presented.

2 Literature review

2.1 Digital and generative design

Before holding the Non-Standard Architectures Exhibi-tion at the Pompidou Center in Paris, the concept of non-standard, non-normative and non-repetitive design was only a theoretical focus of digital design, however, holding the Non-Standard Architectures Exhibition at the Pompi-dou Center in Paris [8]. The generative design had been an essential tool adopted in computer science and in later years, architecture, engineering and construction indus-tries [9].

In last decades, emerging technologies have begun to influence important concerns in design theories, engaged with the exploration of complex geometries, and pro-cesses of fabrication and manufacturing technologies. Different aspects of design such as theoretical, concep-tual and methodological contents of design have been influenced by these developments [10]. Three steps are defining in process of generative design, including a set of rules or schema, a way for variations to develop, and specific outcomes that the variations need to meet [9]. Generative design uses nonlinear systems similar to natu-ral processes, resulting endless unique and unrepeatable design alternatives [3]. The use of state-of-the-art digital technology in architectural design allows users to utilize iterative processes that prioritize form-finding over form-making. Using these tools and techniques allows designers to challenge traditional methods of architectural composi-tion and study the behavior of complex systems [11]. Com-putational design involves the use of abstract logic to find abstract solutions, and for this purpose, the parameters are used to obtain the solutions [6].

Capabilities of generative and performative processes in design have been enhanced in comparison with paper-based methods [10]. Generative design is a designer-driven and parametrically constrained design exploration process operating on top of the parametric CAD systems structured to support design as an emergent process [4]. Generative programming is a style of computer program-ming that uses automated source code creation through generic frames, classes, prototypes, templates, aspects and code generators to improve programmer productivity [12]. Different generative models are identified and categorized based on the type of the generative design process [10]. However, there is a knowledge gap in theoretical frame-work for generative design [4].

The structural principles and features found in natural organisms can be transformed into architectural applica-tions. The geometries and their integration of functions are transferred to architectural applications [13].

Generative design is capable of mimicking nature’s evo-lutionary process using the computer’s power, resulting novel and efficient alternatives of design. The most impor-tant function of generative design is using automation in design process and form generation. Also, the creation of forms that are inspired by nature by using algorithms is one of generative design utilities [9].

The continued growth of geometric design space for architectural applications by advancements in fabrica-tion methods rarely leads to the creation of new systems beyond the typologies of design and construction [13]. Overall, generative design can be described as a method of generating form, using rules, algorithms and often by computational tools [3].

2.2 Geometrical principles of crystallization

Fister Jr, Iztok, et al. in their research provided a list of phys-ics and chemistry-based algorithms as nature-inspired algorithms. For algorithms that are not bio-inspired, most have been developed by mimicking certain physical or chemical laws. These algorithms include electrical charges, gravity, river systems, etc., and different natural systems are relevant to this category [14]. The algorithm crystal-lization process can be placed in this category.

There are several primary rules of crystallization in nature. The primary packing rule for molecular crystals is maximizing density and minimizing free volume. Also, most organic molecules crystallize in low-symmetry space groups. In contrast, most elemental metals and many inorganic salts crystallize in high-symmetry groups. However, the difference is a consequence of the shapes of the packing units and of the presence or absence of strong electrostatic interactions rather than of any fundamental difference in the packing rules

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followed by organic and inorganic materials. Also, inver-sion centers are favorable for crystal packing because they diminish like–like interactions and are uniquely compatible with translation. The operation is unique in that it changes the direction, but not the orientation, of intermolecular vectors [15].

The difference between the formation potential of an unsaturated chemical solution and the solid crystal form is the main driving force behind crystal formation. This is usually simplified by showing the nucleation and growth kinetics of supersaturated saturation, which is the difference between the concentration of solution and the concentration of saturation. Over-saturation is typically caused by the formation of crystals by cooling, evaporation, or by adding a solvent. The challenges of crystallization control are many, and there are consider-able uncertainties regarding their kinetics. Part of the problem is that the kinetic parameters can be sensitive to small concentrations of contaminated chemicals, which change over time [16].

Studies and designs inspired by crystallization have been done in recent years. Engineers of The Water Cube, a swimming pool in Beijing constructed for the 2008 Olympics, considered a variety of arrangements from living cells to mineral crystals [17].

Finally, they designed the structural system based on arrangement of the natural formation of soap bubbles and high technology biomimicry [18].

3 Methodology

In this research, modeling and simulation methods have been used, and the rules of crystallization are simulated with the digital design approach. The stages of the crys-tallization algorithm are shown by a flowchart in Fig. 1. To simplify the simulation process, a base module utilizes a random point placed in a space with a defined domain. The distance of the center of each surface is then meas-ured to the point, and the closest surface is chosen as the host surface. The growth of modules in the early stage is randomized, and a vector is considered for any face of the module. From the second iteration, each module is first mapped to all existing faces, and it is checked that there are no intersected modules. Then, the previous process is repeated for surfaces that can be mirrored without inter-section. In the following, the levels that can be expanded from are specified in the created algorithm. This growth process can continue to infinity. Continuing this process by controlling the designer’s limitations for this algorithm is controlled. The number of iteration of this loop is con-trolled by the designer and is defined as input data for the algorithm.

There are a few rules that affect crystallization. These rules include:

• The number of existing atoms in the environment in supersaturated state.

• The rules of connections between atoms and how atoms bond together.

Fig. 1 Form-finding algorithm

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• The number and location of cores starting and growth of crystallization.

The factor that is deleted from the algorithm in this research is time factor. Decreasing the speed of modules release results in higher accuracy in form.

Primary random points, the modules geometry and loop iterations are considered as input data in the algo-rithm and the output data are a geometrical form. In fact, the factors that make this design method controllable are the base module, iteration number and the algorithm created by the designer. If any changes are needed in design process, the designer can change the algorithm.

In this paper, the fabrication method is not consid-ered, and this method focuses on design. For this pur-pose, the rules of crystallization are modeled geometri-cally by an algorithm in Grasshopper software, which is a visual programing language and consists of iconic ele-ments that can be interactively manipulated according

to some spatial grammar and is also one of the most commonly used generative design editors [10, 15].

4 Case study

To illustrate the results of this research, a pavilion has been designed by the developed algorithm. The stages of form generating by a specific module are shown in Table 1.

In first step, a random point is placed in a space with a defined domain. In next step, a base module with different faces to make more connections possible is defined. Then, the growth of modules in the early stages is randomized, and a vector is considered for any face of the module to provide connection possibility for all faces. The growth process can continue to infinity and is controlled by itera-tion number according to designer’s decision.

Using this algorithm with modules with different shapes leads to different growth patterns. In Table 2, a number of these modules and how the form grows using

Table 1 The stages of generative design 1 A random point placed in a space with a defined domain

2 A base module with different faces to make more connections possible

3 The growth of modules in the early stages is randomized, and a vector is considered for any face of the module

4 The growth process can continue to infinity

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the modulus shown. Based on the chosen geometry for the modulus, this growth can be cumulative or linear.

Three supports were considered for this pavilion on the ground, and the algorithm run in 32 iterations (Fig. 2). This

iterative procedure resulted in a form that can define an architectural space (Fig. 3). This loop was repeated only 32 times, due to the time consuming computing process. Crystals grow from the side of each support and move toward each other to form a cover. Every two modules are connected by a joint surface helping to make connections more structurally possible.

5 Conclusion

The form-finding rules in nature can be converted into form-finding algorithms by computer-aided design tools through different methods. In this study, the rules of crys-tallization in nature were converted to an algorithm in architectural form-finding using digital design tools. Using the method developed in this study led to the design of a pavilion. However, this devised method has some limi-tations. In the process of transforming the form-finding rules of a natural phenomenon into an algorithm, the gap between the two might be so large that it no longer resembles the original idea. Using this design method, the required function of the form may be affected, and its esthetics and shape will prevail. In any case, there is a need for a balance between form, function and structure. In this regard, according to the designer’s view, the algorithm can be modified. In this method, the algorithm begins con-cerning random points, which leads to generating various alternatives. Also, the choice of different geometric mod-ules leads to different behavior in the form.

In this paper, numerical or experimental analysis of the structure has not been conducted. In future studies, after initial form-finding, other factors affecting the design, such as the static and buildability of the model, can be inserted in the algorithm by structural analysis and algorithm modi-fication. Considering the possibility to orient the growth path of the form, it is possible to generate new dynamic alternatives with respect to the amount of solar radiation and shadow, which can be used to design coverings in

Table 2 The stages of generative design tested by different mod-ules

1

2

3

4

Fig. 2 The primary form of pavilion after 32 iterations Fig. 3 The render of the pavilion

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open urban spaces. Also, the accumulation of modulus and their growth path can be made according to structural considerations such as the density of modules in places with higher structural stress.

This algorithm can be used as a plugin in the Grass-hopper Software using a programming language such as Python. However, these findings present only a first step in understanding the natural process of form-finding and converting it into an algorithm. Therefore, it has not been expected to result a form, similar to crystal. Being unpre-dictable to some extent, it is one of generative design properties. This paper aimed at simulation the process of form-finding.

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflict of interest.

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