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The geometrical data structures of links (links to unknown)

A new reading of mereological discourse has been invigorated by the work of philosopher Levi Bryant. Bryant develops the notion of a flat ontology' while discussing the relations of parts to a whole. Flat ontology refers to a lack of hierarchy between units, attempting to conceptualize objects as possessing a fundamental autonomy between one another.21 In holistic sets, what dictates the relationships between the parts is a hierarchical relation to the whole. The discrete paradigm resonates closer with the ideas presented by Bryant, where each unit, defined with its own autonomy, can operate in relation to other parts in a multiplicity of scenarios. An approach for discrete design needs to be able to identify and capitalize on this simple principle: a unit could be designed with its own autonomy in mind, anticipating and maximizing the millions of speculative encounters with other units. The unit is capable of establishing relations with other units but is not defined by its relationality.

To illustrate the ontology' of an open-ended discrete system we will use as an example the Braun Lectron Kit (Figure 3.14), a pedagogical system developed in 1966. The Braun Lectron is a building set for electronics. The system uses principles of electrical engineering to allow a non-expert user to experiment and create sophisticated operational assemblies. The Braun Lectron kit was a discrete set of electric units, each of them containing a series of magnetic connections that would allow them to snap to each other via flat magnetic faces.The set contains functional units belonging to a generic electric system, such as resistors, modulators or speakers. The product is described as follows:

Lectron is an electronic learning and experimentation system. It consists of standardized modules with magnetic contacts. Each Lectron-block contains an electronic component or a connecting line. Through meaningful juxtaposition of blocks arise functional circuits with standard-compliant diagrams.22

Braun Lectron System by Georg Gregor, 1960s.The kit offers a series of building blocks for electronics that can be combined using a magnetic connection

FIGURE 3.14 Braun Lectron System by Georg Gregor, 1960s.The kit offers a series of building blocks for electronics that can be combined using a magnetic connection.

Source: Image courtesy by Michael Peters

Braun Lectron System by Georg Gregor, 1960s.The kit offers a series of building blocks for electronics that can be combined using a magnetic connection

FIGURE 3.15 Braun Lectron System by Georg Gregor, 1960s.The kit offers a series of building blocks for electronics that can be combined using a magnetic connection.

Source: Image courtesy by Michael Peters

While no unit could do much on its own, by arranging these “electronic dominos” into a specific pattern, a user—often a child—would be able to construct a functional system, such as a radio. The radio configuration is one of the many recipes offered to users to learn how to combine units into different arrangements. Functional configurations might only use a subset of units from the kit, as all pieces are not needed to make a whole. This approach lends itself to the discovery of new patterns by both expert and non-expert users. Units can only achieve autonomy if they are designed with a multiplicity of scenarios in mind. As is the case with many discrete systems, in the case of the Braun Lectron kit, there is special attention given to the properties of the joint. The standardized joint establishes a protocol of communication and compatibility between units. While the anatomy of a unit can change greatly, the principles of the joint need to remain the same.

The Braun Lectron kit has been an innovative product that has greatly influenced the development of contemporary toys such as Little Bits (Figure 3.16 and 3.17) by Ayah Bdeir or robotic kits such as Cublets or Moss by Modular Robotics. In the case of Little Bits, we see the development of an entire language of parts that establish their own grammatical patterning. Here joints are also standardized, but the anatomy of the modules allow them to break free from the grid configuration previously presented by the Lectron Kit. This doesn’t make Little Bits any less discrete, as discreteness does not imply a repetitive or uniform pattern of aggregation. On the contrary, it identifies that discreteness is fundamentally a protocol of

Little Bits, designed and created by Ayah Bdeir. The toy is an Open Source library of modular electronics that snap together using magnets

FIGURE 3.16 Little Bits, designed and created by Ayah Bdeir. The toy is an Open Source library of modular electronics that snap together using magnets.

Little Bits, designed and created by Ayah Bdeir. Little Bits, operating as a discrete system, relies in the combinatorial possibilities discovered by crowds to design electronics

FIGURE 3.17 Little Bits, designed and created by Ayah Bdeir. Little Bits, operating as a discrete system, relies in the combinatorial possibilities discovered by crowds to design electronics.

connectivity and compatibility between parts that are strangers. These examples further advance the notion of “combinatorial surplus” as a value proposition of parts, defined not in their implemented relationality but in a potential relationality that is open to unexpected couplings.

Projects such as the Braun Lectron Kit, linked to Gershenfeld’s notion of digital materials, start to define a fundamental distinction between the legacy practice of discreteness—e.g., standardized screws, beams, timber—and the new practice of digital discrete that is aware of the capacity of geometry to define a data structure. Each unit establishes a series of possible indexical relations to other units, allowing for the computation of a body map starting at any point of the network. In contrast to the parametric model, which utilizes an extrinsic data structure, the discrete model is in itself a data structure, offering the opportunities for data modeling operations and potentially local behaviors without a centralized form of control.

An example of this has been the adoption of voxel structures as spaceframes in architecture. Voxels are three-dimensional arrays of data, often understood as three-dimensional pixels. The data structure establishes a series of expected rules, like the neighboring conditions that a unit can have. In the case of an orthogonal voxel, each unit will always have 26 neighbors unless the unit is in an edge condition. Here the problem of conceptualizing data structures prior to units takes us closer to the notion of the whole. Data structures operate as a protocol of a potential whole, rather than predetermining its outcome. They allow the notion of the whole to remain in an open-ended condition.

There is a specific data structure that is flexible enough to establish the foundations of what we have been describing as Discrete Architecture: the graph.

A graph is constituted between nodes and edges. A node is able to establish any number of relations with other nodes represented by an edge or line between them. The edge implies a protocol of compatibility, or a relation established between units. Any form of Discrete Architecture should be able to be diagrammed using graphs, where elements are described as nodes and linkages are represented by edges. From this perspective, we are starting to reveal a picture of Discrete Architecture that develops the notion of“indexical parts,” i.e., parts that are within functional patterns. Patterns contain the principles of a data structure and are able to identify which part belongs where, and how each part relates to other parts. Emerging from the structure of an assembly, the index defines the autonomy of a pattern as an information construct.

The work ofBenJenett and Kenneth Cheung at the Center for Bits and Atoms at MIT, with their BILL-E robotic platform (Figure 3.18), sees discrete design as an opportunity for distributed robotics. The design of small robots that can navigate the structure they build, constituted of small discrete units, points out how discrete design offers an opportunity for automation. In architecture. The Research Cluster 4 at Bartlett School of Architecture in London, led by Gilles Retsin, Manuel Jimenez Garcia and Vicente Soler, aims to align discrete design with automation, designing units that consider the protocols of robotic assembly. In the work of their cluster (Figure 3.19), we see a move away from centralized robotic manufacturing and a turn toward distributed robotics. This move is also visible in the

MIT Center for Bits and Atoms and NASA Ames Research Center. BILL-E robotic platform by Benjamin Jenett and Kenneth Cheung. Discrete lattice built by small distributed robotic system

FIGURE 3.18 MIT Center for Bits and Atoms and NASA Ames Research Center. BILL-E robotic platform by Benjamin Jenett and Kenneth Cheung. Discrete lattice built by small distributed robotic system.

“PizzaBot (2018) is a fully autonomous construction system that explores possibilities for automation in the building sector

FIGURE 3.19 “PizzaBot (2018) is a fully autonomous construction system that explores possibilities for automation in the building sector. B-Pro Research Cluster 4, the Bartlett School of Architecture, UCL. Tutors: Gilles Retsin, Manuel Jimenez Garcia, Vicente Soler. Students: Mengyu Huang, Dafni Katrakalidi, Martha Masli, Man Nguyen, Wenji Zhang."

research “Distributed Robotic Assembly for Timber Structures” (Figure 3.20) led by Ramon Weber and Samuel Leder at the Institute of Computational Design and Construction in Stuttgart. These projects capture the distributed potential of discrete design, one in which multiple agents are able operate simultaneously. Nevertheless, exploiting the distributed nature of discrete design through automation reintroduces hierarchical control and misses the opportunity of allowing a discrete framework to remain open to for a multi-actor economy.

We still need to define how patterns emerge and acquire meaning from a design perspective. As the continuous paradigm utilizes parametric design to modulate and articulate the intensities of flows and surfaces, the discrete paradigm will need

Ramon Weber, Samuel Leder, Distributed Robotic Assembly for Timber Structures, 2018

FIGURE 3.20 Ramon Weber, Samuel Leder, Distributed Robotic Assembly for Timber Structures, 2018.

to identify the design strategies to engage the patterning of units. This will be described here as combinatorial design.

 
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