Visualizing making: Shapes, materials, and actions

Visualizing making: Shapes, materials, and actions Benay G€ursoy, Faculty of Architecture, Istanbul Bilgi University, SantralIstanbul, 34060, Istanbul, Turkey € Mine Ozkar, Faculty of Architecture, Istanbul Technical University, Istanbul, Turkey The increasing interest in materiality currently challenges the long existing traditions that consider visual thinking as the primary actor in design creativity. Shape grammars offer a formalism to represent visual reasoning in design, which is never purely limited to the visual aspects of design processes. Aiming to develop ways to explicitly include material manipulation in a computational formalism, we report on an ongoing exploration of how shape computation extends beyond abstract visual shapes to incorporate material shapes that have a physical existence. We present a materially informed process with shape rules and show that we can apply these rules creatively to explore the physical character of the material. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: material computing, computational models, design activity, parametric design, reasoning

M

aking in design can be defined as a computational process. Firstly, computation can be understood as a general reasoning process, beyond the use of computers. Secondly, design is a reasoning process with aspects that can be traced through computation, in particular visual computation. Thirdly, making is not a discrete stage of design but an integral part of a design activity; hence, it can be defined as a part of a computational process. In this paper, we first outline the terms making, design, computation, and the relations between the three to subsequently argue for new types of computational formalisms to include material aspects of design additional to the visual ones. Our particular focus is on the dukta case as we attempt to formalize a series of physical interventions. Dukta is a novel technique in which sheet materials gain variable flexibility by regularly staggered incisions. Physical manipulation (that is, stretching, compressing, twisting, rotating, bending) of the incised surfaces result in emergent textures or different three-dimensional configurations of the cut parts in space.

Corresponding author: Benay G€ ursoy benaygursoy@gmail. com

Developments in digital fabrication technologies and materials science over the last decade have fostered an increasing interest in materials, materialization, and production processes in design. This interest is currently challenging www.elsevier.com/locate/destud 0142-694X Design Studies 41 (2015) 29e50 http://dx.doi.org/10.1016/j.destud.2015.08.007 Ó 2015 Elsevier Ltd. All rights reserved.

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the understanding of design as a visual thinking process. The distinction between design and making is reconsidered as the available computational tools provide new opportunities for designers to work with actual materials in full scale. Design is associated mostly with the production of abstract representations e drawings or models e to be materialized afterwards. Now making has a renewed role in design thinking. Within an environment enriched by the multifaceted and ubiquitous discussions around the use of digital fabrication technologies, it is necessary to define a framework for making in design that considers its mediating roles between the ideation, representation and materialization processes.

1

Making and design

According to the distinction of design and making in the Renaissance, design is an intellectual and immaterial activity. For Alberti, design is a ‘product of thought’ requiring ‘the mind and the power of reason’ and ‘it is quite possible to project whole forms in the mind without any recourse to the material, by designating and determining a fixed orientation and conjunction for the various lines and angles,’ possibly with the aid of drawings (1988 [1452]: pp. 5e7). Robin Evans (1997: p. 156) observes that architects, even five hundred years later, ‘never [work] directly with the object of their thought, [they] always [work] at it through some intervening medium’ which is almost always ‘the drawing’. With the technological innovations in tools and modes of representation in the Renaissance, drawing became essential to design practice early on. The widespread use of paper and pencil as drawing tools and the invention of planar geometric projection and perspective as modes of representation introduced a fundamental change in the concept of design and in the role of the designer. It was possibly the beginning of an ocularcentric tradition, with the eye becoming ‘the centre point of the perceptual world’ (Pallasmaa, 2005: p. 16). By ‘intensifying the intellectual labour over manual labour’ (Hill, 2005: p. 14), drawing replaced the master builders with designers. Master builders were artisans such as carpenters and stone masons working directly with the objects of their thoughts, while designers represented their ideas for threedimensional forms with drawings accurate enough to be executed subsequently by workmen. The physical model is another type of visuospatial representation frequently used by designers. Working with physical matter to represent design ideas introduces certain material aspects beyond representational purposes. Although always with some level of abstraction and simplification (Dunn, 2007), physical models, beyond the material undertaking of a design idea, serve as design tools that promote thinking as well as communication between the designer and the design (Smith, 2004). These aspects can be employed for a variety of reasons. Alberti (1988 [1452]: p. 34) for instance, points out the use of the

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physical model for evaluative and predictive purposes. The former enables the designers to ‘examine the work as a whole and the individual dimensions of all the parts’ while the latter helps to calculate the estimated costs by taking the scaled elements as reference. Cannaerts (2009) distinguishes architectural models as ‘models of architecture’ and ‘models for architecture’ regarding how they inform the design process. Models of architecture correspond to the representational models made after the design process. They are interpretative rather than explorative. Models for architecture, on the other hand, are explorative. They correspond to the working model, sketch model, or the conceptual model made during the early stages of the design process and ‘are part of the iterative process of representation and interpretation’ (Cannaerts, 2009: p. 782). G€ ursoy (2010) discusses models for architecture as a form of early design sketching. Inherent uncertainties in physical model-making, either because of the accidental moves or because of the unpredictable behaviours of the materials, lead to the generation of novel ideas in the design process. Antoni Gaudı and Frei Otto, for instance, used models not only to represent the visuospatial aspects of their design ideas, but also to investigate the performative properties of materials that guide the generation of three-dimensional form. Instead of imposing materiality to a preconceived form, Gaudı and Otto explored ‘materiality both as genesis and fabrication of [architectural] form’ (Voyatzaki, 2015: p. 14). In this paper we look at making in general, that is, the formation, production, and construction of the material thing itself, rather than model making. Following Cannaerts’s distinction for models, we distinguish making of and making for by taking into consideration the mediating role of making in the ideation, representation, and materialization sequence. In making of, design ideas are conceived in representational media such as drawings and digital models, and materialization involves the processing of the information available in these representations. Within this framework, materialization does not inform the design process and the focus is on the seamless connection between design representations and their full-scale material outcome. In making for, on the other hand, making and design are not separate. Making shapes design ideas and the designer values the exploration realized through making. Rather than the end product, the focus is on the improvisational process and the unexpected discoveries that occur due to the properties of materials and techniques unforeseen in abstract representations. Materialization denotes not only the processing of information, but the processing of materials as well. There is an alternating dialogue between the control in making of and the uncertainty in making for that parallels the differentiation David Pye (1968, pp. 20e24) makes between the ‘workmanship of certainty’ and ‘workmanship of risk.’ Pye explains the difference between the two by comparing modern

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printing and writing with a pen. Where the result of printing is predetermined, the act of writing with a pen involves a risk. The result of penmanship is not fully controlled, but unveils uncertainty through controlled direction or intention. Although we believe in the richness of the dialogue between the control in making of and the uncertainty in making for, in this paper, we concentrate on delineating making for and its contemporary place in design computation. The making for framework challenges not only the design traditions that put idea over matter but also the contemporary understanding of design as a computational visual reasoning process. We aim to extend the latter by identifying the computational aspects of design processes shaped as much by making as by visual reasoning.

2

Making in design and computation

Most of the prominent studies of design feature visual aspects and approach design as a way of visual thinking. The pattern of seeing, acting on it, and then seeing something else during designing is implied in the generative specification of paintings by Stiny and Gips (1971) and has been at the core of shape grammar formulation since. This pattern is also recognized in the ‘see-move-see’ model advocated by Sch€ on and Wiggins (1992). Sch€ on (1983) depicts the designer in a ‘reflective conversation with the situation’ (p. 76) and in a visual interaction with abstract representations of the design problem. His interpretation has been widely accepted and has fostered much research on the externalization of design thinking in drawing and sketching. Goldschmidt (1991) similarly refers to a dialogue in design sketching between ‘seeing that,’ corresponding to reflective criticism, and ‘seeing as,’ corresponding to analogical reasoning. We define design as a conscious activity of establishing relations between parts to achieve unity. The possibilities for constantly defining new relations or redefining the existing ones make design a creative process. In the visionoriented understanding of design, the key to design creativity is frequently deemed to be the ambiguities inherent in the visual perception of shapes. Interpreting new shapes and reinterpreting new meanings correspond to the ‘seemove-see’ model of design where the designer acts upon his/her reflection on the visual representation of shapes. Utilizing shape ambiguities in visual representations then becomes an integral part of designing. The uncertainties in the visual perception of shapes are especially significant in Stiny’s computational theory of shapes (2006). Here, the ambiguity is the result of some basic attributes of shapes. Shapes do not have definite parts and can be divided into parts in any number of ways enabling the viewer to see embedded shapes within shapes. One can always see something new in a shape: ‘the way the shape was made and how it is divided into parts afterwards are independent’ (Stiny, 2001: p. 24). With this capacity, shape computations, as recursive applications of shape rules, support the non-linear process of

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design. In the course of a shape computation, the designer can choose which shapes to see and which rules to apply in a manner that reflects the ‘seemove-see’ model of design where ‘moving’ connotes the application of shape transformations. While computing with shapes provides a rich playground for designers, Stiny’s visual reasoning, or spatial reasoning in its comprehensive version (Stiny, 1980), elevates the design thinking that is ‘knowing without reasoning and bringing it into the world of reason’ (Martin, 2009). Design as reasoning allows the implicit design ideas to become explicit, enabling their communication with others. This is mostly crucial in educational settings and in design studio crits to establish a dialogue between the instructors and the students. € Ozkar (2011) suggests that the externalization of visual reasoning in design through the shape formalism is useful in first year design studios for raising students’ awareness of their own design processes and for providing a common ground to talk about design as a computational process. Additionally, through conscious reasoning, designers establish relations between parts to build up a whole. The design becomes a relational system instead of a unique and one time outcome, and thus designers can generate variations if necessary. Lastly, reasoning enables designers to guide and anticipate emergence. As opposed to ‘accidental emergence’ (Oxman, 2002), emergence in visual reasoning processes is ‘anticipated’ and occurs with the recognition of shapes. By being able to distinguish between accidental and anticipated emergence, designers can first recognize the unexpected discoveries occurring throughout the design process and then turn them into design moves. Similar to seeing, any exploration with making introduces to design some unforeseen outcomes of physical intervention. In pioneering studies within the new material computing research area, material practices commonly appear at the center of design activity. In these studies, materialization and computation are linked through advanced technologies (Menges & Schwinn, 2012) and making is enhanced as ‘new digital design practice introduces computational thinking’ to it (Thomsen & Tamke, 2009). Nevertheless, current studies that bring together materials and computing often limit them both to the mere use of digital tools rather than acknowledging their role in reasoning. The technical interfaces of digital tools offer rigorous and imposed formalisms that handle known material properties. Still, there is a lack of computational formalisms to represent the sensory aspects of working with materials as there is in shape grammars for seeing and working with shapes.

3

Formalizing making in design

Formalisms enable conversations with oneself as well as with others. For design processes dominated by visual thinking, shape computations provide formal descriptions that give insight into processes of shape transformations

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and ‘a process model for the externalization of visual reasoning in design’ (Oxman, 2002: p. 134). There are, for instance, studies that represent explorative sketching (Prats, Lim, Jowers, Garner, & Chase, 2009) and physical prototyping (Paterson, 2009) in a design process with shape rules, providing formal descriptions of creative design processes based on objective external evidence rather than designers’ retrospective verbalizations of their thought processes. Visual schemas, as more generalized versions of shape rules, are suitable for talking formally about particular design knowledge in an educa€ tional context (Ozkar, 2011). Applications of visual rules and schemas do not yet represent the feedback from material interactions in making for processes. In making for, designers often make use of other senses to augment their visual interaction. Although limited to hands-on making of sculptural works, a related study shows that in the making of hands-on works, much of the significant perceptual information is provided by haptic senses, while vision monitors the progress of the process (Prytherch & Jerrard, 2003). Therefore, designers’ interactions with material things, either through hands-on processes or digital fabrication tools require extended visual formalisms. There is a need for visual representations that capture the full range of interactions that designers employ as they explore and discover the properties of material form. Recently, Knight and Stiny (2015) proposed to extend the shape grammar formalism from shapes to ‘material things’. Another recent study reports on bending experiments with cardboard sheets to explicitly include variables of materials in the computation of € form making (G€ ursoy, Jowers, & Ozkar, 2015). This paper is positioned along similar lines as we aim to clarify the translation of material manipulations to shape computing.

3.1

Dukta: shaping sheet materials for variable flexibility

We present a particular case of making for in which sheet materials gain variable flexibility by regularly staggered incisions. Although frequently referred to as the dukta technique since its invention in 2006, methods to shape stiff sheet materials in three dimensions existed earlier on with names such as kerfing and living hinges. The name dukta derives from the terms ductility and duktus, the former being the ability of a material to be stretched or shaped without breaking, and the latter signifying an artist’s characteristic style of drawing, especially the drawing of lines (Kuhn and Lunin, n.d.). In this paper, we adopt the term dukta to define the framework of our material explorations in making sheet materials flexible. The dukta case is suitable for showing the performance of a surface varying based on shape and material property. The material aspects observed in dukta are open to exploration once the cut patterns are generated, indicating two discrete but causally interrelated phases. The first phase employs visual transformations that constitute the patterns for cutting. The effect of these visual

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features on the material affordances and constraints is usually unpredictable as they are mostly created either with insight or without considering materiality. This first phase leads to trial and error processes or accidental discoveries during material interventions of the second phase. The physical interventions in dukta are mostly spatial displacements of the overall form and its parts with actions such as bending, stretching, folding, compressing, and twisting. The process is short and simple, and embodies controlled actions that can easily be traced. Additionally and most importantly, it yields emerging shapes that are characteristic of design processes. These emerging shapes correspond to textural variations on the sheets, as well as spatial displacements of the parts resulting in three-dimensional form configurations. Existing material explorations in dukta can employ top-down approaches that value the end product over the process. Woodweaver, a computer-based parametric modelling system, for instance, has a top-down approach to the dukta technique where users design a curved surface and the software generates the dukta cut pattern, which when materialized with stiff wood boards, can bend to the form of the curved surface designed (Ohshima, Igarashi, Mitani, & Tanaka, 2013). The design of the cut pattern is not defined through material constraints but through geometric relations of shapes to cut, with the clear goal of fabricating the defined curved object without using moulds or glue. The accuracy between the end product and its digital representation is of utmost concern, and making involves the assembly of the fabricated parts, indicating a making of process. On the contrary, our approach to material explorations in dukta is bottom-up as we aim to decipher the causal links between interventions with the material and our shape making. Below, we first depict the visual schemas and the shape rules that generate a selection of existing dukta cut patterns. Using these rules, we generate our own series of dukta patterns which we then cut out of cardboard to obtain material samples. By physically manipulating the material samples, we systematically and comparatively explore the material affordances and constraints provided by the dukta patterns. We represent the physical actions to extend the use of shape computation from abstract shapes to material shapes.

3.1.1

Generating dukta patterns: transformations of visual

shapes Certain visual schemas and shape rules generate a variety of existing dukta patterns. We observe that rules that result in diverse applications of the dukta technique fit under three of the general schemas Stiny has already introduced (2011): x / x þ tðxÞ (Schema 1) x / prtðxÞ

(Schema 2)

x / tðxÞ

(Schema 3)

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In dukta, Schema 1 copies and translates a shape, providing the repetitive arrangements of the shapes common in all dukta examples. Schema 2 decomposes a shape into several parts and erases certain parts. The erased parts become the hinges specific to the dukta technique. While the first two schemas are essential for dukta pattern generation, the third schema enables the creation of more variations. These schemas represent the general characteristics unifying and diversifying the dukta patterns and are especially useful for denoting these characteristics formally. The unifying formalism of schemas enrich the transformations confined to more specific rules, providing a high-level visual language to describe transformations in the generation of dukta patterns. In Figure 1, we provide an example of the most common shape rules used in dukta, where x in the schemas correspond to a shape made up of lines in 2D. Rule 1 and Rule 2 fall under Schema 1 (Figure 1-a) whereas Rule 3, Rule 4, Rule 5 and Rule 6 fall under Schema 2. In the latter group, the line in the left-hand side is split into parts and some parts are erased. The four different rules identify which different parts are erased (Figure 1-b). Rule 7 falls under Schema 3 and is used to rotate the line in the left-hand side of the rule (Figure1-c). Rules in Figure 1-d, Figure 1-e, and Figure 1-f replace the lines with other shapes. Unlike the previous rules, these three rules are not described well with a general schema. They are rules for substituting shapes particular to dukta patterns. Note that rules in Figure 1-d can also be interpreted as changing the weight (line width) of the lines in the left-hand side. Figure 2 showcases the uses of the rule transformations in shape computations to generate the basic dukta patterns. Rule 1 and Rule 2 control the density of the patterns (Figure 2-a). Rule 3, Rule 4, Rule 5 and Rule 6 are applied to the shapes obtained after the recursive applications of Rule 1 or Rule 2. These rules split the lines into parts and erase some parts. The erased parts are not cut during materialization and become hinges that connect the cut parts of the material samples. Even with only these six rules, we can obtain a large number of variations (Figure 2-b). The recursive application of Rule 7 changes the direction of the pattern (Figure 2-c). The remaining rules in Figure 1-d, Figure 1-e, and Figure 1-f introduce additional variations, and have considerable effects on the density of the surface, resulting in significant textural variations, as exemplified in Figure 2-d. The first set of dukta patterns that we have generated using the rules above are shown in Figure 3. The illustrations are organized in a matrix to highlight which combination and ordering of rules generate each pattern and how the generation of each pattern relates to the entire set. All patterns start with the application of either Rule 1 or Rule 2. The variation continues in the next step as Rules 3, 4, and Rules 5 and 6 together are applied. The result is six different patterns, three for each track following from the first step. Rules 7, 8, 9, and 10 are then applied to each of these six outcomes to produce

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Figure 1 The first set of rules employed in generating the dukta patterns: (a) Rule 1 and Rule 2 copy and translate a line vertically. (b) Rule 3, Rule 4, Rule 5, and Rule 6 split a line into parts and erase some parts. (c) Rule 3 rotates a line. (d)e(f) Three sets of shape rules that replace lines with other shapes

twenty-four patterns. In these illustrations, each pattern is bounded by a uniform rectangle that represents the boundaries of the sheet material. In all patterns, there are uncut parts at the bottom and the top of the rectangle. The rules under the schemas can be populated infinitely to generate variations. In Figure 4-a and c, we present additional Schema 1 rules with polylines and equilateral hexagons in the left-hand sides. The rules in Figure 4-b and Figure 4-d fall under Schema 2. They split the left-hand side shapes into parts and erase some of the parts. Note that the shapes in the left-hand sides of the rules in Figure 4-d are parts of the equilateral hexagon. We generate a second set of dukta patterns using these rules. The outcomes are illustrated in Figure 5. Infinite possibilities exist in the generation of dukta patterns. The shape computations that generate these patterns can be altered in many ways. Defining new rules under the aforementioned three schemas, changing the sequence of the rules, as well as the iteration count can have significant effects on the resulting patterns. The rules frame the variations and provide an understanding and control of the pattern generation process. In the following section, we present a formal model to represent our physical interventions with the materialized dukta samples. We extend the use of visual rules and schemas from representing abstract shape transformations to representing the transformations of the material shapes in 2D and 3D space.

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Figure 2 (a) Computations with Rule 1 and Rule 2, (b) computations with Rule 3, Rule 4, Rule 5, and Rule 6, (c) a computation with Rule 3, and (d) three computations where the lines are replaced with other shapes

3.1.2

Material manipulations: transformations of material

shapes While different cut patterns expand the scope of possible outcomes, types and specifications of the materials used also have tremendous effect on the material constraints and affordances. The dukta technique is suitable for sheet

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Figure 3 The cut patterns generated with the first set of rules

materials such as wood, cardboard, plastics and metals. For the material explorations, we produced our samples using 0.2 mm cardboard. This translation from abstract shapes to material shapes is shown in Figure 6. Working with the material samples, we recognize that the material manipulations in dukta are mostly related to the displacement of its parts in space. Moves such as stretching, compressing, bending, folding, and twisting require flexibility. These moves translate and/or rotate certain parts of the samples. The translation and rotation of the parts can be in 2D or 3D, resulting in different three-dimensional configurations of material shapes.

Shapes, materials, and actions

39

Figure 4 The second set of rules employed in generating the dukta patterns: (a) Rule 11 and Rule 12 copy and translate a polyline vertically. (b) Rule 13, Rule 14, Rule 15, and Rule 16 split polylines into parts and erase some parts. (c) Rule 17, Rule 18, Rule 19, and Rule 20 copy and scale an equilateral hexagon. (d) Rule 21, Rule 22, and Rule 23 split polylines (which are parts of the equilateral hexagon) into parts and erase some parts

The material samples we produced consist of a perforated (cut) area in between two uncut areas. While the uncut areas do not change their shape during physical interventions, new material shapes emerge in the perforated areas either as textural variations or through displacements of its parts in space. These emerging shapes are perceivable only through a physical intervention. With the aim of formally modelling our physical interventions with the dukta samples, we extend the use of visual rules from representing abstract shape transformations to representing the transformations of the material shapes in space. We represent the uncut areas with abstract shapes and formalize our physical interventions as transformations of these shapes. The process this time is a translation of material shapes back to abstract shapes. An example of this translation can be seen in Figure 7. The abstract shape obtained in Figure 7 can be transformed in space in many ways. For the scope of this paper, we present a limited set of rules to show the transformations in 2D, on a plane (Figure 8). In these rules, the bottom rectangle provides a context for the transformation of the top rectangle. A label is placed on the translated top rectangle to deal with the ambiguities concerning the orientations of the transformations. The use of this formalism can be two sided. While it serves to represent our physical interventions with the samples, it can

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Figure 5 The cut patterns generated with the second set of rules

also be used creatively to generate new configurations of the parts. Note that in Rule 28 and Rule 30, the top rectangle moves onto the bottom rectangle. Shapes do not fuse as in set grammars such as the one defined for physical play with Kindergarten blocks (Stiny, 1980). Physically, a hand holds the bottom area of the sheet material in place while the second hand moves the upper area in

Shapes, materials, and actions

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Figure 6 Left: the abstract shape. Right: the corresponding material shape

Figure 7 Left: the material shape. Right: abstract shape representing the uncut parts of the material shape

Figure 8 Eight shape rules

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space to lay it flat on top of the bottom one. The physical act of aligning the edges of the rectangles in our example is similar to the use of index finger and thumb to align two blocks in Kindergarten grammars. The shape rules in Figure 8 correspond to what the hand does to the material shapes in space. The abstract shapes in the rules represent the dukta patterns, and material shapes stand for themselves. With the rules in Figure 8, we translate material shapes back to abstract shapes to represent the transformations of the uncut parts of the samples in 2D space. After shape computations with these rules, we translate abstract shapes to material shapes yet again. The abstract shapes on the left and right sides of the shape rules define the start and end of the manually caused deformations in the material shape. The end results in the material shape account for a process of making for. The back and forth translations between abstract and material shapes can be followed in Figure 9 and Figure 10. In Figure 9, the eight rules from Figure 8 are applied to manipulate the same material sample. Differently in Figure 10, one rule (Rule 24) is applied to different material samples. The exception is the rules in Figure 10-f and Figure 10-g, which are modified versions of Rule 24. New material shapes, indeterminable unless materially manipulated, emerge in the cut areas through the displacement of parts in space. Note that the outcomes would be different with different materials. Design specifications of the dukta patterns impose material affordances and constraints, enabling some samples to easily stretch, compress, or bend and some to resist these actions. With no definite design goal in manipulating the samples, we use this formalism to unveil the affordances and constraints imposed by the design specifications of the cut patterns and to understand why they occur. We use the computational formalism to reason about material manipulations in making. This approach also allows us to handle uncertainties concerning how materials behave and to anticipate emergence in material shapes. In Figure 9-a (and in Figure 10), the translation of the rectangular shape with Rule 24 indicates material stretching, while Rule 25 in Figure 9-b indicates compressing. The rotations in Figure 9-e and g with Rule 28 and Rule 30 are not common transformations in dukta explorations. The exploration with the abstract shape representation of the uncut parts of the material samples results in an uncommon spatial relation between the two rectangles and sequentially in the overall spatial form of the cut parts. This shows how the switching back and forth between abstract and material shapes leads to creative outcomes and that the process is not a making of something but rather a making for. The far right column of Figure 10 shows that samples materialized from different cut patterns behave differently under the same type of

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Figure 9 Different shape rules to manipulate the same material sample

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transformations. Significant textural variations emerge within the cut areas. The first material sample (second column from the left in Figure 10-a) is generated using Rule 2 under Schema 1. The other material samples in the same column used in the subsequent computations are generated either with Rule 1 or Rule 11 under the same schema: the pattern is considerably less dense with larger parts in the cut area, and as can be seen in the outcome (far right column in Figure 10-a), it resists to stretching more than others. The emerging openings are smaller and the upper uncut rectangular part cannot be translated as much as indicated by Rule 24. While the second cut pattern (Figure 10-b) is generated with Rule 1 (Schema 1) and Rule 5 þ Rule 6 (Schema 2), additional rules are employed in the generation of the third (Figure 10-c), fourth (Figure 10-d) and fifth (Figure 10-e) cut patterns, all replacing the lines in the second pattern with other shapes. When materialized, the samples in the third and fourth cut patterns already have hollow shapes, which enlarge further when stretched. The use of the additional rules in the fifth cut pattern does not bring as much variation as in the other two examples. The lines in the cut patterns used in the last two examples (Figure 10-g and f) have different orientations, which also impact the outcomes: the emerging hollow shapes follow the orientation of the lines. The systematic approach to the generation of the cut patterns as well as the manipulation of the material samples enables comparative explorations where each exploration reveals certain attributes about material affordances and constraints, leading to a deeper understanding of the making process in dukta. More comparative explorations of this type can be realized by manipulating the material samples through transformations in 2D and 3D. The patterns generated with the hexagon rules in Figure 4-c result in material samples that do not conform to transformations in 2D. In Figure 11 we present two examples with two new rules. The first column shows the initial abstract shapes that are generated with iterative applications of Rules 18 and 20, respectively. We first materialize the cut patterns as shown in the second column from the left. Representing the boundaries of the inner and outer hexagons with abstract shapes, we translate the inner hexagons vertically in 3D with Rule 32 and Rule 33. The material outcomes of these translations can be observed in the far right column in perspective, top, and bottom views. Even though the exact same lines are cut on both samples, the configuration of these lines defined in the first column with the use of Rule 18 and Rule 20, both under Schema 1, significantly changes the material outcome. The material sample with the concentric pattern (Figure 11-a) stretches straight up vertically with the same openings emerging on each side. The other sample with the translated centers (Figure 11-b) stretches up at an angle and its openings are of different sizes. Once again, a very small variation in the rule results in big variations in the material shape. Although it is possible to predict the results to some extent, especially as one becomes accustomed to the rules

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Figure 10 Different material samples are manipulated with the same shape rule ((a)e(e)). The exceptions are the last two ((f) and (g)) where the rules are variations of Rule 24 with modified shapes

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and materials at hand, the performative aspect of handling the material shape in the last stage prevents a determinate result. Hence we deem this process as making for.

4

Discussion

Reviewing the role of making in contemporary design thinking, we present at the beginning two frameworks, namely making of and making for. The first framework values control and accuracy in the processing of information. The second values uncertainty in the processing of materials much as in the visual reasoning that shape grammars record for design computation. It is this second framework that we have focused on in this paper. While visual rules and schemas are well suited for formalizing visual reasoning in design, existing applications do not yet represent the feedback from material interactions in making for. We look at a particular making for case in which sheet materials gain variable flexibility by staggered, regularly arranged incisions, referred to as the dukta technique. The variability depends on changes in material specifications, design specifications of the cuts, and the physical interventions employed. New material shapes emerge when dukta samples are materially manipulated. These are open to discovery only through making. Our study with the dukta case involves two discrete but interrelated stages. In the first, we classify the visual rules employed in the generation of existing dukta patterns with reference to the unifying formalism of schemas. We argue that formally representing the dukta pattern generation process serves as a basis for further bottom-up approaches in designing dukta patterns while providing a common ground for systematically exploring the material outcomes of these patterns in relation to one another. The key challenge of the study lies in deciphering the causal links between our shape making and interventions with the material so that both can be represented in shape rules for computation. Therefore, in the second stage, we explore the ways in which shape computation can extend beyond abstract visual shapes to represent material shapes that have a physical existence. Through several explorations involving transformations of the material samples in 2D and 3D, we represent our physical interventions and apply shape rules creatively. The systematic formal approach in the generation of the dukta cut patterns and in the material manipulations enables us to comparatively explore the material affordances and constraints imposed both by the design specifications of the cuts and the properties of the materials. At the same time, we are able to produce creative outcomes by switching back and forth between abstract and material shapes in simple examples of dukta cases. Designers’ explorations with dukta often focus on increasing the flexibility of stiff sheet materials. While being able to regulate the flexibility of the materials can be considered valuable in design, we claim that, as designers, our explorations with dukta

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47

Figure 11 From left to right columns: abstract shapes, corresponding material shapes, shape rules translating in 3D the abstract shapes that represent the inner and outer hexagons of the material shapes, and the material outcomes of these translations viewed from perspective, top and bottom

can expand beyond concerns for flexibility. Quantifiable material properties such as flexibility are more suitable for computer generated simulations. We recognize emerging shapes as variations in texture and emphasize some haptic aspects of design as we cut and manipulate the material samples. Our study is limited to one material and a finite number of rules. Further explorations can compare results with different materials and rules for a deeper understanding of making processes. Further research can also expand to plastic manipulations of material such as hand-made pottery where causal links between material and form creation are even more direct. Such cases are especially challenging as visual abstractions to serve as intermediaries are mostly missing in current practices. For this paper, we have focused on showing that employing computational formalisms in making for processes leads us

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to reason about the process. We utilize the uncertainties in how material things behave and anticipate emergence in material shapes. The shape formalism we employ is by choice unspecific and intuitive and serves the purpose of representing our actions in general terms rather than giving exact descriptions for a computer implementation. Nevertheless, these rules are specific enough to compare with one another and produce the corresponding changes in the results. Our formal approach can be especially valuable in design studio environments where communicating ideas is necessary for learning. Any haptic exploration such as bending, stretching, folding, and twisting a physical object is sensory and personal. These aspects often remain incommunicable. Formal representations of the process that cover as much of its full sensory breadth as possible would enable informed and resourceful conversations among students and between students and instructors.

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