(from The Interior Architecture Reader, edited by Gregory Marinic, 2018 Routledge)

Chapter 18

Transforming interior volumes

Volume + surface + mass

Jonathon R. Anderson and Laura Lovell-Anderson

In the inextricable design continuum, form and function are balanced by science and mathematics as variables to design and realize objects, environments, and experiences. The result is a shift in systems of knowledge, thinking, and problem solving within interior architecture – a paradigmatic fluidity – emerged through the coupling of traditional tools and emergent software and digital fabrication. These digital technologies and processes yield unprecedented capabilities, allowing for physical and fabricated realization of designs that were once considered too complex or unbuildable. Through an amalgam of these techniques and technologies integrated within digital design and physical prototyping, designers are defining interior volumes using surface mathematics to develop autogenic design topographies at the interior scale and context. It is a practice that emphasizes the value of both the process and product through experimentation to challenge the designed surface and interior screen,

exploring the spatial characteristics of designed surfaces as tangible installations through an approach combining aggregates or modular component-based systems to manipulate volume, surface, and mass.

Agent-based visual scripting and computation is used as a medium for experimentation, decision-making, and problem solving to formulate dynamic surfaces and topographies. The digital design process expresses an algorithm to intervene in a system and segment a complex design query into several simplified sub-problems, and later reconstructed to create a solution.$^1$ To further underscore this concept, Wilensky concludes, “by enabling the rendering, simulation and visualization of the evolution of complex systems over time, the computer has proved an indispensable tool for making sense of complex systems and emergent phenomena.”$^2$ Accordingly, emergent computational form-generation approaches to design applied in conjunction with digital and physical making encourage the examination of the complexities that compose natural forms and their corresponding internal geometries.

The process of transforming an interior volume in a realized, visual expression may rely on systems that are either abstract (intangible; concepts, theoretical notion) or physical (defined by material nature). This chapter, however, as a survey of the emerging process for transforming interior volumes through the development of autogenic design topographies at the interior scale and context, focuses on physically expressed systems. The formula for developing autogenic systems of design starts simply: shape < surface < volume. In the most primitive sense, shape is the two-dimensional primitives such as points and lines; surface is an interconnected set of points and lines that have length and breadth; and volume is the three-dimensional space enclosed by a collection of surfaces.$^3$

Transformation of the interior volume through a systems-based approach requires the understanding that a system, a “set of elements or parts that is coherently organized and interconnected in a pattern or structure,” is the logical basis for defining and transforming interior volumes via visible surface mathematics.$^4$ Individual characteristics of a system – the components, constraints, interrelationships, interface, boundary, purpose,

environment, input, and output – when aggregated, produce a pattern or structure within a system, representing an expression of an observed regularity, and exist in both biotic and abiotic systems. Systemic articulation of such a set of elements or behaviors is used to form aggregates or modular component-based systems and, therefore, manipulate volume, surface, and mass. Geometric transformations, resulting from the physical expression of surface mathematics, are often simulated through a process of cell aggregation to generate volume. Such practices of extreme computational control have emerged across various design disciplines, impacting both form and function. It serves to realize relationships between entities, develop surfaces and membranes, understand complexity and patterns of behavior, and add functionality.

The design process of transforming interior volumes requires the application of concepts of autogenic design and systems theory to develop a model, an abstract representation of system developed to aid in the understanding and/or predicting of its behavior. The next sequence in transforming the interior volume is the modeling process, a rigorous method for creating and testing models. Systemic (and rule-based) computation and visual-spatial scripting are where a series of nodes or agents at the micro-level are extracted from a data source. The visual representation of such is produced through modeling, characteristically in a collection of small components to ultimately compose one larger surface. Emerging design scholarship describes the process to be characteristically autogenic, where “auto,” is a prefix meaning “of oneself,” and “genic,” is an adjective meaning “produced or generated by.” Autogenic can, therefore, be understood as an object, system, or process that is characteristically self-generated or self-produced, and in such a formula, these variable inputs allow for the calculated manipulation of the surface parameter, environment size, and variations in the number of nodes or agents. However, such transformation requires a hybrid process combining foundational design elements – volume, surface, and mass – with both spatial geometries and systems theory.

These systemic components are organized into larger surfaces or screens to form aggregates or large amounts of unbound elements lying in loose

frictional contact, therefore subdividing a system into smaller parts that can be independently created and used in different systems.11

Systemic theory and computation as applied to spatial systems in interior architecture and design allow for the conceptualization, modeling, and fabricated realization of designs that were once considered too complex or unbuildable.12 Accordingly, form and function are generated and informed methods previously used exclusively in science and mathematics sectors; these approaches as applied to design in conjunction with digital and physical making encourage the examination of the complexities the compose natural forms and their corresponding internal geometries. In the example of “Self-Organizing Cuticular Structures of Butterfly Wing Scales in Callophrys rubi,” such an application of systems theory and modeling for the manipulation of system characteristics can be applied to formulate interior logic and architectural patterns.

Academic case study of The Gyroid: An Investigation of the Self-Organizing Cuticular Structures of Butterfly Wing Scales in Callophrys rubi

A precedent assembly by Janine Yeung, under the supervision of Professor Jonathon R. Anderson at Ryerson University School of Interior Design and completed in spring 2016, The Gyroid reflects an autogenic design topography that was generated through analysis and systemic computation of a surface. This work is based on the repetition and subdivision of a cell and submodules of a gyroid surface to which input parameters from a biotic system consisting of a 50% fill density and 50% porosity were applied.13

In the systemic development of the interior volume, the base geometry was a micro component within the larger macro surface to be contained within a cube to ultimately be aggregated through tiling in the mathematical logical of self-organization. This was achieved by extracting a series of the surface’s edge curves, then mapping the edge curves on the

faces of the cube, in a manner that also attempts to preserve the vertices of the surface by assigning these to the corners of the cube. The optimized geometry is a locally minimized surface that contains six vertices and six curved edges, where each edge is in contact with a unique face, and each vertex is in contact with a unique corner (Figure 18.1).

The autogenic systemic input data as applied in The Gyroid was derived from the occurrence of the gyroid structure in natural nanostructures, specifically in the analysis of wing scales in the butterfly species Callophrys rubi, where the cuticular structure adopts the gyroid form (Figure 18.2). The butterfly wings of this species are composed of chitin, a polymer prevalent in organism exoskeletons. In this species, these structures are organized in gyroid forms to produce structural coloration and the effect of iridescence when light moves through these geometries. The gyroid nanostructures are composed when chitin (which polymerizes in the larval stage of the species) is deposited in the extracellular space of a scale cell (double gyroid). Following chitin deposition, the cell degenerates and is transformed to a single gyroid structure, leaving an interconnected network of chitin in air. The resulting chitin network satisfies a condition of 50% structural volume and 50% air or porosity. This parameter becomes the primary input that will be applied to the submodules. By integrating these parameters, the autogenic characteristics of the biotic system interact with the self-organizing logic of the mathematical surface to produce the final component geometries.

Figure 18.1 System characteristics – the components, constraints, interrelationships, interface, boundary, purpose, environment, input, and output – organized to produce a pattern or structure

Image credit: author

Figure 18.2 Shape developed through a series of autogenic systemic inputs and unit subdivision. Volume resulting from self-organizing logic, as demonstrated through the shape grammar and assembly of cellular gyroid units. The subdivision of larger surfaces to develop a series of simple modular forms.

Image credit: author

The conceptual framework consists of three parts: input of micro-level emergent phenomena to delineate spaces, simulation of simple shape grammars in visual scripting, and an output for visualizing the loop-based calculation by the various micro-level emergent phenomena and macro-level patterns. Using emergent software including K3DSurf, Yeung input a series of isosurface constraints and parametric equations to produce surfaces, and alter Cartesian values to manipulate existing surfaces, where $x = 1.5$, $y = 1.5$, $z = 1.5$ in the trigonometric approximation: $\cos(x) \cdot \sin(y) + \cos(y) \cdot \sin(z) + \cos(z) \cdot \sin(x) = 0$. A paradigmatic fluidity emerges through a process and

product of experimentation through the manipulation of aggregates or modular component-based systems. The result is a topography and spatial geometry where the physical systems are visually self-organizing into a distinctive three-dimensional pattern.

The autogenic processes applied for spatial organization allows that “designs and their meanings [can] be viewed as the results of computations carried out according to rules of composition and correlative rules of description.” From the data inputs generated from the modeled systems, the physical and visual outputs may be realized through the coupling of traditional tools and emergent software and digital fabrication through both additive and subtractive means. The output can be translated through analog and digital means, with an array of modeling or physical prototyping realities.

Designers are defining interior volumes in an emerging hybrid process that combines foundational design elements – volume, surface, and mass – with both modular component-based systems and spatial geometries to manipulate autogenic design topographies. The application of such processes facilitates paradigmatic fluidity in the systems of knowledge, thinking, and problem solving in interior architecture and in the generation of complex systems and patterns. Incorporation of these processes of transforming an interior volume, as evidenced in the academic case study The Gyroid by Janine Yeung, reflects the value of systemic articulation as a method for problem solving, especially in an academic environment and undergraduate curriculum.

In a design studio charged with exploring the application of defined interior volumes with surface mathematics to develop autogenic design topographies at the interior scale and context, the outcome was a study of surface generation to imply volume and mass, controlled through input parameters and systemic components. Through an amalgam of analog making techniques and emergent digital making technologies, including digital design and physical prototyping, students explored the spatial characteristics of designed surfaces. Students worked in small collaborative groups to experiment with and challenge the designed surface and interior

screen through an approach combining aggregates or modular component-based systems to manipulate volume, surface, and mass. Through this process, students applied concepts of autogenic design and interior volume transformation to design a collection of small components to ultimately compose one larger surface. Coupled with traditional tools, emergent software, and digital fabrication, the transforming of the interior volume nurtures the exploration of the spatial characteristics of designed surfaces as tangible installations.

Figure 18.3 Through the interior volume transformation process, Yeung reflected: “there is often an ambiguity between invisible and defined boundaries in mathematical surfaces – and this may translate to factors of the component in regards to overall geometry relating to form flexibility. An initial subdividing process may introduce parameters necessary for the component design, including the general shape and the number of vertices in each module (dependent on the method of subdivision). This process stems from the notion of ‘self-generated’ modular forms as a result of a

subdividing process. The outcome should ideally allow for an articulate component organization about a substrate” (2016, p. 12).

Image credit: author

Notes

1 Donella Meadows, Thinking in Systems: A Primer (White River Junction, VT: Chelsea Green Pub., 2009); I.M. Rocker, “When Code Matters”, Architectural Design 76 (2006): 16–25.

2 Uri Wilensky, “Modeling Nature’s Emergent Patterns With Multi-Agent Languages”, Proceedings of EuroLogo 2001 – Linz, Austria, 2001.

3 Lionel March and George Stiny, “Spatial Systems in Architecture and Design: Some History and Logic”, Environment and Planning B: Planning and Design 12, no. 1 (1985): 31–53.

4 Donella Meadows, Thinking in Systems: A Primer (White River Junction, VT: Chelsea Green Pub., 2009), p. 187.

5 Donella Meadows, Thinking in Systems: A Primer (White River Junction, VT: Chelsea Green Pub., 2009).

6 Lionel March and George Stiny, “Spatial Systems in Architecture and Design: Some History and Logic”, Environment and Planning B: Planning and Design 12, no. 1 (1985): 31–53.

7 Donella Meadows, Thinking in Systems: A Primer (White River Junction, VT: Chelsea Green Pub., 2009).

8 Uri Wilensky, “Modeling Nature’s Emergent Patterns With Multi-Agent Languages”, Proceedings of EuroLogo 2001 – Linz, Austria, 2001.

9 Evan Douglis, Autogenic Structures (New York: Taylor & Francis, 2009); L. March and G. Stiny, “Spatial Systems in Architecture and Design: Some History and Logic”, Environment and Planning B: Planning and Design 12, no. 1 (1985): 31–53.

10 Jonathon Anderson and Laura Schoenthaler, “Materializing the Digital Realm”, in Textile Technology and Design: From Interior Space to Outer Space, ed. D. Schneiderman and A. Winton (London and New York: Bloomsbury Publishing, 2016).

11 Michael Hensel, Achim Menges, and Michael Weinstock, Emergent Technologies and Design: Toward a Biological Paradigm for Architecture (New York: Routledge, 2010).

12 Evan Douglis, Autogenic Structures (New York: Taylor & Francis, 2009).

13 Janine Yeung, “The Gyroid: An Investigation of the Self-Organizing Cuticular Structures of Butterfly Wing Scales in Callophrys rubi”, Prepared for Professor Jonathon R. Anderson, IRN 800

at Ryerson University School of Interior Design, 2016.

14 Lionel March and George Stiny, “Spatial Systems in Architecture and Design: Some History and Logic”, Environment and Planning B: Planning and Design 12, no. 1 (1985): 31–53.