Topological Interlocking Assembly: Introduction to Computational Architecture

Abstract

Topological interlocking assembly (TIA) and computational architecture treat form as an emergent property of a material system, where the final shape results from the interplay of geometries and geometric interdependencies influenced by contextual constraints (material, structure, and fabrication). This paper posits that TIA is an ideal pedagogical tool for introducing students to computational architecture, and its theoretical foundations and design principles. Specifically, defining TIA as a material system provides a robust educational approach for engaging students with computation; fostering design processes through bottom-up, hands-on investigations; expressing design intents as procedural logic; understanding generative geometric rules; and exploring the flexibility of parametric variations. The methodology is detailed and illustrated through a design workshop and study unit from the Bachelor’s and Master’s programs at the Faculty for the Built Environment, University of Malta. Four case studies of TIA—of tetrahedra, cones, octahedra, and osteomorphic blocks—demonstrate how these exercises introduce students to computational thinking, parametric design, and fabrication techniques. This paper discusses the advantages and limitations of this pedagogical methodology, concluding that integrating computational architecture in education shifts students’ design processes to investigation and innovation-based approaches, enabling them to address contemporary design challenges through context-driven solutions.

1. Introduction

The notion of topological interlocking assembly (TIA) was introduced by Yuri Estrin and Arcady Dyskin to material science in 2001. Since then, architecture has embraced it, where its structural, aesthetic, and spatial potentials have been interpreted and explored [1,2,3,4,5,6]. This assimilation has accelerated TIA’s research, development, and applicability. This paper argues that TIA is particularly significant for computational architecture and identifies two key potentials of its inherent behavior: as an educational research tool and as a material system.

The first potential reflects the increased educational relevance of computational architecture, evident in the current curriculum of several leading architectural schools, such as MIT [7], Royal Danish Academy [8], UCL [9], and EPFL [10], which have shifted their focus towards this area. This shift reflects a broader rethink and critical reconsideration of digital technology in the architectural design process, aiming to enhance the current state of the art [11,12]. Within this shift, Tessman [13] successfully engaged TIA geometrical investigations in a design studio, providing an experimental educational platform for students to develop computational design processes through hands-on investigations. Building on this research, this paper presents a pedagogical methodology designed to further exploit the educational benefits of TIA geometric investigations. However, the limited examples of the use of TIA in computational educational contexts necessitated a trial-and-error approach to develop the methodology, highlighting a research gap that this paper addresses.

The second potential engages the TIA constituent geometric relationships. A TIA is defined by an identical configuration of its elements, their mutual arrangement, and a boundary constraint that holds the whole assembly together [14] (Figure 1a). Elements’ configuration necessitates the alternating rotation of their contact faces to generate the interlocking principle (Figure 1b). In this way, the arrangement of elements in TIA imposes local kinematic constraints, uniquely keeping each element locked in its position solely by the geometrical constraints of its adjacent elements. This distinctive feature, except for the elements at the assembly’s periphery, prevents the removal of each element by either upward, downward, sideways, or rotational displacement by its neighbors [14]. In short, a TIA works as a system of geometries and geometric interdependencies from which the assembly’s form emerges. This approach parallels computational architecture, which treats form as an emergent outcome of a system. Computational design processes abandon the traditional Modernist linear approach where the form and its aesthetic dictate structure and material choices. Instead, they synthesize the form from spatial, structural, and material principles [15]. Thus, the focus is not on the manifested form, that which appears, but on the material system from which the form emerges. The material system is an interaction between internal rules that embed the form and external morphogenetic pressures activated by contextual feedback [16]. The computational architectural theoretical discourse lacks recognition of the link between TIA and the material system, representing the second research gap that this paper addresses.

With the proposed methodology, this paper aims to contribute to the practical and methodological discourse in architectural education. Firstly, by focusing on TIA’s constituent geometries, the methodology seeks to expand students’ spatial skills. Furthermore, the methodology’s integration of computational theory and experimentation enables students to assimilate unfamiliar concepts, such as TIA, within their design processes and enhance their creative thinking [17]. Finally, this paper discusses the methodology’s advantages and limitations, emphasizing a critical perspective as intrinsic to the computational approach [18]. In doing so, this paper advances the understanding and application of TIA in computational architecture, enriching both architectural education and practice and laying the groundwork for future exploration and innovation.

From the theoretical perspective of computational architecture, a TIA is a typical example of a material system. For this reason, this paper argues that the TIA is an ideal pedagogical tool for introducing students to computational architecture, and its theoretical notions and design principles.

2. Fundamentals of Computational Architecture

Computational architecture approaches design problems through systemic thinking and derives solutions, or a range of solutions, through bottom-up design processes.

Systemic thinking is a holistic examination of broadly applicable interaction patterns that underlay, drive, and govern a system. Contrary to reductionist thinking, where a whole is divided into parts, systemic bottom-up thinking recognizes the overall global arrangement of parts as a cohesive, synergetic distribution of their dependences. The system’s behavior is expressed through emergent generative processes.

Computation focuses on problem formulation and process expression, from which a solution or a range of solutions is derived. Computation can both describe a process through the inner principles of its activity and a plug-in into the process’s activity, its unfolding [19]. The computational design process seeks to define a system of generative rules, a material system from which it derives solutions. The material system consists of internal rules and external adaptation. The internal rules are based on the relationships between the material system’s constituent elements, while external adaptation is based on contextual feedback. The derived, manifested form is a relative actualization of the material system’s relationships [20].

An algorithm can describe the material system’s internal rules that comprise embedded forms [16]. Computation formulates a material system’s algorithm. Firstly, its bottom-up processes discretize constraints through their underlying mathematic, geometric, syntactic, and formal logic [15]. Next, its procedural logic externalizes these constraints and their interdependencies as generative rules.

3. Introduction to Computational Architecture: Methodology

This paper presents a methodology for integrating systemic thinking and computation into architectural design processes, with two primary aims.

The first aim is to challenge traditional reductionist design thinking and linear, top-down architectural design processes. The methodology incorporates iterative investigations and computation to establish design processes that prioritize problem formulation and the expression of these processes, from which a solution or a range of solutions emerges. This approach contrasts with the established methodology in the current pre-tertiary educational system, where students are often led to pursue a single, final solution. This mindset tends to persist as they develop their design processes.

The second aim is to introduce theoretical geometric processes that enhance students’ spatial understanding and proficiency in transforming between two-dimensional representations and three-dimensional forms, and vice versa. Akin to descriptive geometry, the learning objective is to accurately represent three-dimensional objects on a two-dimensional drawing [and computer screen] and deduce their exact definitions and respective positions [21].

This methodology engages TIA as the primary tool and investigative platform to achieve its aims. Understanding a TIA proves more complex than initial impressions suggest. While students often feel confident in grasping its principles through observation and visual comprehension, challenges arise when tasked with 3D modeling a TIA due to its intricate geometries and geometric interdependencies. TIA presents an unfamiliar concept where established solutions or thinking patterns do not apply. Instead, its definition requires a procedural understanding of its formation process.

The methodology focuses on TIA’s geometries and geometric interdependencies: the interlocking principle generated by the elements’ configuration of the alternating rotation of contact faces and their mutual arrangement. Unlike similar academic exercises that engage TIA and address structural issues (boundary constraints and force flows) and buildability (jointing, assembly process, and falsework) [13,22,23,24], this methodology emphasizes the formation process and the emergent forms resulting from TIA’s system of generative geometric interdependencies. It approaches TIA through systemic thinking, conceptualizing it as a procedural synthesis of spatial principles. In essence, the methodology formulates and evaluates TIA as a material system.

3.1. Defining TIA as a Material System

The methodology for defining TIA as a material system consists of two iterative steps, each informing the other: understanding and discretizing TIA’s internal rules and formulating them into an algorithm. With each iteration, students gain knowledge that directly informs their design decisions, further explorations, and evaluations.

In the first step, students use physical scale models to expand their understanding of the geometries of individual elements, the overall assembly, and their interdependencies (Figure 2). Here, the TIA is approached as a spatial arrangement that is concurrently a whole subdivided into parts and propagation of parts that generate a whole. Students, thus, have to concurrently understand and define geometric rules that govern the relationship between individual elements and the procedural rationality of the assembly as a whole.

In the second step, students express the geometric rules formulated in the previous step as an algorithm and run it several times to validate it. Students can run the algorithm through analogue or digital means. Each algorithm run entails systematic variations of inputs (parameter values) and students’ rigorous recording of outputs through cataloguing. The algorithm outputs also provide fabrication information for prototyping. Finally, students further assess emergent forms expressed by catalogues and prototypes to address the TIA material system’s versatility and limitations.

As the concluding step, students are prompted to envision the TIA material system’s architectural potential. Proposals leverage the material system’s inherent adaptability and transformative qualities beyond TIA’s original design intentions and construction decisions. Design proposals solely explore TIA’s geometric interactions and interwoven aesthetics rather than the practicalities of constructability and structural plausibility. Architectural speculations aim to enhance students’ control of the formation process and spatial understanding by manipulating TIA’s geometries and geometric interdependencies. Students understand that their investigations are not realstic applications as they do not address buildability, detailing, and structural stability (Figure 3).

3.2. Methodology Outcomes

The methodology is intentionally non-prescriptive, fostering students’ individual understanding of the investigated TIA and its underlying generative geometric rules. As a result, the algorithms are varied, leading to a diverse range of formal outcomes, each with unique variations and limitations. While the resultant forms appear different, they are unified by the same underlying generative rule: the TIA interlocking principle. The divergence among projects is acceptable and encouraged, as the methodology prioritizes individual interpretations and explorations over pursuing a single correct solution.

In the same way, when assessing student work, the focus is not on how accurately their algorithms replicate the specific TIA investigated. While achieving the interlocking principle is essential, students must demonstrate a thorough understanding of the formulated material system, including its versatility and limitations. The goal is not for students to develop a material system that actualizes all given parametric inputs but to cultivate a deep understanding of the material system’s generative rules. Students are expected to grasp the range of inputs the material system can actualize and evaluate the capabilities of these outcomes. Specifically, students must show control of the formation process, the geometric generative rules they defined, and the geometric properties of resultant forms. They need to identify scenarios where these rules do not work and explain the reasons behind these “failures” of the formation process.

In this way, defining a TIA as a material system becomes a versatile academic exercise and a valid pedagogical approach that enables students to engage in computation; develop design processes through bottom-up, hands-on, iterative investigations; express design intents as procedural logic; understand generative geometric rules; and explore the versatility of parametric variations.

This methodology is illustrated using four case studies from Bachelor’s and Master’s programs at the Faculty for the Built Environment, University of Malta. Three studies showcase how a year 2 BSc design workshop introduces computational thinking and parametric design. The fourth study demonstrates how AUD5641 Architectural Technology 2, a year 2 MArch study unit, integrates computational design and fabrication. These case studies highlight the practical application of this methodology, demonstrating its effectiveness in enhancing students’ computational skills and design capabilities. By engaging with TIAs, students gain a deeper understanding of both theoretical and practical aspects of computational architecture, preparing them for advanced design challenges.

4. Computational Design Workshop

The Computational Design Workshop was an elective 3 ECTS, seven-week (half-semester) design workshop in year 2 of the BSc (Built Environment Studies) program between 2013 and 2016. Its primary learning outcome was introducing students to computational thinking and parametric design. Dr Irina Miodragovic Vella, one of this paper authors, was the coordinator and tutor, while the co-tutors over the years included architects Jing Yao Xu and Kane Borg. It followed the described methodology to analyze a specific TIA typology, define it as a material system, and then investigate its potential for adaptation and transformation. The task was developed as group work that allowed students with varied skills and interests to take ownership of the aspect of the project that aligned with their affinities. The three TIA topologies investigated were TIA of tetrahedra, TIA of intersecting cones, and TIA of octahedra.

Investigations involved formulating algorithms using digital parametric models of associative geometry. Parametric models were developed through visual programming using Grasshopper, an associative modeling plug-in for Rhinoceros Version 5 3D software. Software facilitated and enhanced computation to generate and evaluate emergent forms. Parametric models provided fabrication information for physical scale models and prototypes in subsequent iterations and exposed constraints in the assembly sequence. However, the primary focus of the process was not on the software itself. Emphasizing software would limit the conscious recognition of computation as a paradigmatic shift within the [architectural] discipline [28].

The specific input variations investigated included the surface curvature (planar, single curvature, and double curvature) (Figure 4), the angle of the contact face rotation, and trimming planes’ positions. Students recorded outputs through cataloguing to assess the emergent forms and the material system’s versatility and limitations.

4.1. Case Study 01: TIA of Tetrahedra

The TIA of tetrahedra investigation was particularly interesting due to its historical precedent, the Abeille flat vault, which predated the notions of a TIA, computational architecture, and a material system for several centuries.

Joseph Abeille patented the flat vault in 1699 to provide a stone ceiling for the lower storey and pavement for the upper storey with identical voussoirs [29] (Figure 5a). The unique voussoir geometry and the rotation of neighboring voussoirs by ninety degrees allow for a simple method of their mutual arrangement. Each voussoir is carried by two neighboring ones through its protruding cuts while supporting two others on its sloped cuts [21]. The Abeille flat vault is a TIA of regular tetrahedra planarly truncated at their center and some distance below it (Figure 5b). Throughout history, the Abeille Vault has rarely been used due to the high amount of horizontal thrust that required the demanding construction of boundary constraints, like buttresses or massive walls [30]. Students’ investigations developed four distinct procedural logics to formulate a material system, leading to unique outcomes, limitations, and diverse architectural applications.

The first procedural logic derived the tetrahedron from the diagonals of a cube’s top and bottom faces and generated the assembly as an array of tetrahedra (Figure 6). Thus, the procedural logic solely dealt with the assembly as the propagation of parts to create the whole and did not address the assembly as a whole subdivided into parts. The actualization of the resultant material system was limited to a planar surface and regular square gird.

The second procedural logic derived tetrahedra from a rectangular grid on a planar surface using a checkered pattern and rotated lines. The checkered pattern defined two types of tetrahedra, A and B. Each side of every rectangular grid cell had a line rotated around its midpoint. For type A tetrahedra, lines on opposite sides of the rectangle were rotated by an angle α in one direction and –α in the other. Conversely, for the type B tetrahedra, this rotation was reversed (Figure 7).

Following the checkered pattern, type A and B tetrahedra arrayed alternately in the X and Y directions on the planar surface. The procedural logic and algorithm were derived and validated through hands-on investigations using physical working models at different scales. The TIA principle was retained for planar or single-curvature surfaces but not for double-curved ones. Finally, students developed several proposals that speculate the architectural applications of the TIA material system (Figure 8).

The third procedural logic defined the tetrahedron based on planar curves derived from the contouring of a planar or single-curvature surface. The resultant curves, curve c, were approximated with equal linear segments, line a. For each even curve in the array, segmenting was shifted by half the length of line a. Next, each line a was rotated in the curve plane around its end and start points for angle α and –α, respectively. The intersection of the rotated lines, line a′ and line a″, is Point A. Adjacent Point As defined lines b. Line a was also rotated by 90° around its mid-point in the plane normal to the plane of curve c. The rotated line, line a‴, was translated to line start and end points as lines c. Line c was also translated to point A as line d. Lines a and d make the tetrahedron type A (green), and lines b and c make the tetrahedron type B (violet) (Figure 9). The TIA principle was retained for planar or single-curvature input surfaces but not for double-curvature ones.

The fourth procedural logic explored a particular investigation: variations and limitations of the Abeille TIA principle on a geodesic dome (Figure 10). The physical working model allowed students to both understand the assembly sequence and validate the procedural logic (Figure 11). Finally, albeit very conceptual, proposals for the possible architectural applications were developed too (Figure 12).

4.2. Case Study 02: TIA of Intersecting Cones

The TIA of intersecting cones investigation also included a historical precedent, the Truchet flat vault. The Truchet flat vault was developed in 1704 to improve the Abeille vault (Figure 13a). Truchet voussoirs actualized the alternating contact faces’ rotation of the Abeille voussoirs as undulations of concave and convex double-curved surfaces. Thus, the Truchet voussoir configuration was challenging to fabricate until the introduction of contemporary six-axis CAD/CAM tools [32].

For the same reason, the design workshop task asked students to translate concave and convex surfaces into single-curvature surfaces and derive them from the intersection of cones (Figure 13b). Students’ interpretation of the underlying geometric logic of the TIA of intersecting cones resulted in two procedural logics for a material system.

The first procedural logic started with a grid of intersecting cones of radius r and height H (Figure 14a). The grid checkered pattern defined cone types A (light green) and B (dark green). The center C of each cone was at the distance r in the x and y directions from its neighbors. Each A cone intersected four adjacent B cones and was tangent to the next set of A cones. The same applied to B cones. Next, each A cone was trimmed by two B cones in the x direction (Figure 14b) and trimmed by two B cones in the y direction (Figure 14c). Finally, a set of trimming planes, as the offset of the original grid, truncated each cone at its mid-height H (Figure 14e) and some distance below it (Figure 14f). The resulting material system retained the TIA principle for planar or single-curvature input surfaces but not for double-curved ones (Figure 15a). As the final step, students developed design proposals speculating architectural applications of the material system (Figure 15b).

The second procedural logic started with a square grid. Each side of a grid cell was a tangent that defined a circle, the middle of each cone (Figure 16a). In this way, the grid cell sides remained tangents that defined a closed curve even for irregular grid cells (Figure 16b). The rest of the algorithmic sequence followed the first procedural logic: the checkered grid pattern defined cone types A and B; each A cone was trimmed by two B cones in the x direction and trimmed by two B cones in the y direction; two planes, grid offsets, truncated the cones at their mid-heights and some distance below it. Since the geometric rules of this procedural logic allowed for the deformation of the cones, the resulting material system retained the TIA principle for all surface curvatures (Figure 17).

4.3. Case Study 03: TIAs of Octahedra

As with the previous two case studies, students’ interpretations of the TIA of octahedra derived distinct procedural logics for a material system. They differed in how they defined the alternating rotation of elements’ six contact faces to achieve the TIA principle.

The first procedural logic defined an octahedron by connecting the vertices of top and bottom faces, two identical, parallel isosceles triangles. The top triangle was offset by distance H from the bottom and rotated by α = 60° around its centroid. This way, the TIA of octahedra was approached as two parallel fields of triangles, TIA’s top and bottom non-contact faces, elements’ extrados and intrados (Figure 18). The resulting material system retained the TIA principle only for planar surfaces but not single- and double-curved ones. For this reason, the second procedural logic was developed to address this limitation. It introduced a column of infill polygons between the columns of the isosceles triangles. The resulting irregular decagons enabled the material system to be actualized on single-curve surfaces. The procedural logic was validated through investigations of variations and physical models (Figure 19).

The third procedural logic started with a hexagonal grid defining a rotated plane field. Each plane was rotated around a grid cell side by the same angle α but in a direction opposite to the rotation of its neighboring planes. The intersection of the six rotated planes generated an octahedron (Figure 20). The resulting material system retained the TIA principle for all surface curvatures.

5. Computational Design and Fabrication Study Unit

AUD5641 Architectural Technology 2 is a 5 ECTS computational design and fabrication study that is part of the Master’s in Architecture (Architectural Design) program. The study unit coordinators are Dr Irina Miodragovic Vella—one of this paper authors—and architect Steve DeMicoli. It follows the described methodology but with a broader scope. Students need to develop and investigate variations of a material system derived from an overlay of capacities and constraints of multiple aspects: assembly geometry, material properties, and fabrication limitations. A material system is, thus, developed by recognizing and exploring underlying geometries and geometric interdependencies of the individual elements and their overall assembly, but also the versatility and limitations of the given material, fabrication tools, students’ instrumental knowledge, and construction process requirements [34].

Case Study 04: TIA of Osteomorphic Blocks

The limited funds in the academic year 2017/2018 focused the study unit investigations on affordable materials and fabrication. The materials available were sheet materials like paper, cardboard, and plastic, as well as any material that fit within the study unit’s limited budget. The available fabrication tool was a laser cutter. The assembly geometry investigated was a TIA of osteomorphic blocks.

The osteomorphic block was invented for wall and column construction in high seismic zones [35]. Similarly to Truchet voussoir, it actualizes the interlocking principle as multiple alternations of concave and convex surfaces on the voussoir’s horizontal contact faces. Their fabrication, thus, requires six-axis CAD/CAM tools. The running bond construction sequence enables the TIA principle. Its vertical contact faces are planar (Figure 21a).

Students used iterative prototyping at multiple scales and with different materials to investigate how the constraints of the TIA principle, fabrication tools, and material properties mutually inform each other. More precisely, through tail-and-error, hands-on investigations, students gained knowledge that directly informed their design decisions, such as choosing materials and fabrication techniques, further explorations, and architectural applications.

Since the fabrication of the concavo-convex surfaces required six-axis milling, the investigations of TIA geometries and geometric interdependencies had to be rethought from the start within the constraints of the laser’s two-axis cutting abilities and sheet material properties. As a result, elements’ concavo-convex surfaces became planar surfaces rotated in alternating directions. The translation necessitated the formulation of two element types to retain the assembly’s interlocking principle (Figure 21b).

Students had to develop a fabrication technique that ensured the elements’ rigorous geometric definition and contact face planarity. They used a casting process with plaster from Paris and moulds made from laser-cut, folded sheet materials. The mould material had to be suitable for laser cutting, stiff enough to retain the mould’s shape during the cast and contact surfaces free of warps, smooth to enable easy moulding, sturdy enough to be reused for multiple casts, and allow for tooling perforations. Tooling perforations had to allow the mould to fold in two directions (peaks and valleys) without impacting the mould’s stiffness or allowing the casting material to leak (Figure 22a). Iterative prototyping also allowed students to understand the fabrication challenges of scaling up the mould using the same material (Figure 22b). The plaster mix had to be viscous to allow an easy casting process and sharp edges but not seep through the perforations at the folds, create surface wraps, or crack during drying. Iterative prototyping established an interdependency between the plaster’s viscosity and the faces’ rotation angle, stress concentration at the sharp edges, and the length of the casting and drying processes (Figure 23).

An additional procedural logic investigated a single element type with a configuration of no planar faces to increase its degree of interlocking (Figure 24a). Although theoretically, the configuration achieved a more optimal interlocking, the added complexity reduced the precision of its fabrication. The result was unavoidable warping and imperfections of elements’ contact surfaces that prevented interlocking, the principle it was trying to optimize (Figure 24b).

In short, prototype-based investigations exposed material properties and fabrication limitations as external adaptations that hindered internal rules from manifesting the embedded, interlocking forms.

6. Limitations

The case studies also revealed certain limitations in using a TIA as a pedagogical tool.

Firstly, students found some TIA typologies easier to comprehend, leading to variations in the depth of investigations and the versatility of derived material systems. For instance, investigations centered around tetrahedra allowed students to engage in more comprehensive investigations, thus gaining broader design knowledge than students who tackled other TIA typologies.

Next, the tutors’ familiarity with TIA geometries and interdependencies influenced their ability to remain impartial in guiding students towards their unique investigations. Unintentionally, tutors imposed their understanding of TIA’s underlying rules, resulting in less diverse student projects over time. Student investigations became more tutor-led, losing the bottom-up approach driven by personal hands-on knowledge gained with each iteration. Consequently, prescription and similarity supplanted ownership, divergence, explorations, and versatility.

Further, TIA is inherently complex in structure, fabrication, and construction. Students explored TIA material systems for various surface curvatures, focusing on descriptive geometry unrelated to buildability and structural stability. Case studies emphasized investigations of typical geometries and interdependencies of TIA’s constituent elements. They did not address necessary boundary constraints for assembly or their impact on edge and corner configurations. Additionally, fabricating and assembling TIA entail significant costs, posing challenges in proposing realistic and feasible architectural applications.

Finally, the design workshop primarily focused on digital parametric modeling to run algorithms, requiring a steep software learning curve to achieve this. Consequently, students spent most of their time acquiring instrumental knowledge of the software to encode algorithms rather than exploring its generative potential. Instrumental knowledge of the software directly influenced the understanding of TIA and the formulation of its algorithm, making the design process subservient to the digital tool’s limitations. The result limited engagement with computational thinking as instrumental software knowledge, or its lack of, directly enabled or disabled students in the act of design [36].

As a result, the design workshop tasks and methodology have evolved in recent years. The focus has shifted towards defining two- and three-dimensional tessellations as material systems. If interlocking is introduced, it is not topological but planar, reminiscent of M.C. Escher’s work. This approach simplifies investigations but allows for more significant student appropriation, ownership, and customizations. Analogue algorithm formulations use pseudocode and flowchart formats. Investigations are conducted primarily hands on. They inform algorithm formations, output variations, limitations, materiality, fabrication tools and techniques, and on-site assembly sequence.

Students find the architectural applicability of tessellations more intuitive, as they can be applied at various scales while addressing multiple aspects such as program requirements, environmental performance, and aesthetics (façade panels, shading screens and canopies, floor tiling, and pavilions). Students can address the structural principles, architectural detailing, and construction processes of the simplified notions investigated. Still, although the design workshop’s learning outcomes increased in range, students’ geometric investigations have reduced in depth and spatial understanding.

7. Conclusions

Computational architecture discretizes and externalizes context as a system of generative rules, forming a material system from which it derives context-driven solutions. This discipline folds context to establish a material system that subsequently unfolds it within its spatial outcomes. Computational architecture acknowledges and engages with the interdependencies and exchanges inherent in contemporary design challenges by operating on both contexts and content. It adeptly responds to modern contextual tropes of heterogeneity, transiency, indeterminacy, and instability. Consequently, this paper argues that computational architecture should be introduced at the grassroots level of architecture: architectural education.

The proposed methodology offers a potential approach to achieving this integration. Its primary learning outcome aims to transform students’ design processes from a top-down imposition centered on aesthetics and performance to a bottom-up, computation-based approach. It involves investigations and explorations that lead to generative formation processes capable of addressing multiple design constraints. The focus is on problem formulation and process expression, from which solutions, or a range of solutions, emerge.

The design workshop and study unit discussed in this paper illustrate how introducing students to TIA as a material system through computational design principles enabled them to explore and engage with the unfamiliar. On a broader theoretical level, students transcended conventional design thinking to develop processes that interact with and respond to the unknown and uncertain. On a broader practical level, they expanded beyond their established working methods to adapt to the evolving role of the architect demanded by these design processes. The acquired shift in design thinking enables students to effectively incorporate material properties and fabrication machine limitations as parameters in their design processes [37,38]. It opens new avenues for architectural research and educational advancement and enhances architectural production practices.

In conclusion, students derived design processes that are both informed by and tailored to the specific contexts they encountered, demonstrating the validity and relevance of computation for contemporary context and its architecture.