Pablo Miranda Carranza

Pablo Miranda Carranza, Fractal landscape, KTH Royal Institute of Technology, Stockholm, 2014Result of applying a substitution scheme to triangular faces of the mesh. The scheme is a basic graph rewriting rule that substitutes one triangle for four new triangles at each iteration. The new vertices introduced each time are given a random height. Produced using the Open Source Computational Geometry Algorithms Library (CGAL).

PROGRAMS

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How might we synthesise two very different approaches in architecture? One based on programme and another on typology or paradigm. Pablo Miranda Carranza, a researcher at the Architecture School at the Royal Institute of Technology (KTH) in Stockholm, takes his cue from an approach suggested by Colin Rowe in the early 1980s to examine how computation formulates architectural thinking and presentation.

PARADIGMS

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In Program vs Paradigm, Colin Rowes contribution to the second number of the Cornell Journal of Architecture, he suggested a synthesis of what he saw as the two mutually exclusive approaches to design at the time: one based on analysis and facts, which he identifi ed with programme, and the other based on typology and paradigm.1 In Rowes proposed synthesis, types were promoted to diagrams that organised programmatic facts and information, an approach that incorporated the historicity of type, the exactitude of data and the semantic openness of diagram. Th irty years later this mix can be useful in understanding some of the eff ects of the computer in architecture. In a medium in which even geometry needs to yield to the one-dimensionality of data and the sequential logic of computer programs, it is interesting to consider how computation disciplines our thoughts about architecture, how its theories, concepts and material limitations create forms in which architecture is cast.

Type and TechnologyDiscussions of architecture and technology are generally dominated by an emphasis on innovation, in which the study of historical precedents is not a priority. Ideas of paradigm, precedent and type run against dominant discourses of technological progress that emphasise novelty and the state-of-the-art, rather than tradition and repetition of patterns in technological practice. Reyner Banham found it paradoxical that the Parisian avant-garde simultaneously strove both for object-types and technological revolution: while articulating an artistic response to the instability brought by technology with its upheaval of existing models and focus on constant innovation, its theoretical output, particularly through the pages of LEsprit

Nouveau, concentrated on the classic stability of industrial object-types, results of the laws of mechanical selection, function and economy, operating in time.2 Th e dilemma posed by Banham seems, then, either to accept that a technology is old enough to have stabilised into types, or that otherwise it has not had the time to do so and is still new and revolutionary. But technologies are always part of traditions, and are sooner or later stabilised into standard practices and paradigmatic operations.

Th e developments of the very linguistic models that are the basis of computation illustrate a shift of interest from combinatorial innovation to the constraints of tradition: while Ferdinand de Saussures langue and parole or Noam Chomskys generative grammar consider how a fi nite set of signs and rules are capable of generating an infi nite set of sentences, Foucault rather observed how the fi eld of discursive events is fi nite and limited at any moment to the linguistic sequences that have been previously formulated.3 In other words, what we can say now is always dependent on what has been said before.

In the case at hand, the fi eld of discursive events is largely defi ned by the use of computers in architecture and their history, from Christopher Alexanders HIDECS, one of the earliest uses of programming in architecture, to the latest release of Grasshopper, the visual programming editor for the Rhino modelling package. But actually what has been said and can be said through computers is mostly the domain of computer science and engineering, and particularly disciplines like algorithm analysis, software design or computational geometry that deal with the material and practical limitations of implementing the logic abstractions that constitute computation. By far one of the most important aspects to consider in any computer program is its feasibility in terms of space and time, that is, the space in memory and the time it may require to run. Computing time and space are bounded resources4 even if it is commonly assumed that since computers become incrementally faster and memory cheaper, most problems involving memory or time will eventually be solved. Th ere are, on the other hand, many computational problems that no matter how much faster computers may become, or how much available memory they may have, they will unlikely be solvable in any reasonable time for a large enough input. Th us there are many tasks that are not practically tractable through computation.

A number of situations in architecture show this high computational complexity: defi ning the circulation network of minimum length connecting a set of locations in a building or city, also known as the Steiner tree problem, or fi nding the shortest route that visits all locations, known as the travelling salesman problem, are not strictly solvable in any feasible time for a comparatively small number of locations, as they belong to the class of problems known as Non-deterministic Polynomial-time hard (NP-hard). At the same time there are also many methods and algorithms that can be executed in reasonable time for relatively large inputs. Th ese algorithms, together with existing techniques for effi ciently accessing data, constitute the stable schemas that organise the way to represent and analyse space in computers, and for that matter anything else. Th e technological discursive fi eld of computation is formalised in the diagrams resulting from the conceptual and material limitations of computation as a technology.

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Pablo Miranda Carranza, Convolution lter applied to the density of bars and restaurants in Vienna, KTH Royal Institute of Technology, Stockholm, 2014opposite: OpenStreetMap data of location of bars and restaurants in the city, mapped onto a two-dimensional lattice, and smoothed thorough the Weierstrass transform, a standard procedure in signal processing that shows variations of intensity on the input data.

Pablo Miranda Carranza, Fluid dynamics simulation through the lattice Boltzmann method, KTH Royal Institute of Technology, Stockholm, 2014Similarly to cellular automata, the lattice Boltzmann method calculates the density and velocity of a gas at each cell, depending on the densities and velocities of its neighbouring cells in the previous iteration.

Space PerformedTh e notion of algorithm is basic to all computer programming. Disregarding more formal enunciations it is possible to assume that an algorithm is a computation that operates on input data to produce an output: the transformation of a coarse 3D mesh into a smoother subdivision surface, the generation of a spline from control points, the calculation of shortest paths or centrality on the street network of a city, or the stresses and strains on a structure are examples of algorithms used in architecture. Th e way they transform input into output defi nes how architecture is represented through computers, similarly to the way geometry defi nes how it is represented through drawings.

Th e most important of these constraints is the seriality of current models of computation based on the abstraction of a Turing machine,5 a conceptual device that represents a program as a mechanism consisting of a head that can sequentially read and write symbols on a paper tape. Computers are the electronic implementation of a generalisation of this concept, known as a universal Turing machine.6 Th us any representation of architecture in the computer needs to submit to its sequential nature, which implies an ontological problem

about space; extension, in the computer, needs to be reduced to a sequence, both in the way it is stored in memory and in the way it is serially interpreted back into spatial phenomena. Consequently the display of a two-dimensional form on a screen, its printing on paper or its digital fabrication, are the result of the consecutive execution of instructions into perceivable events. Space in the computer always needs to be performed. To do so it has to conform to the schemas developed for its effi cient storage and processing by algorithms. Th ese schemas, known as data or information structures, encode structural relationships between data elements7 as they store and organise data in order to facilitate access and modifi cations.8

Space as Program In architecture, a number of recurrent schemas and patterns, the result of common data structures and algorithms, can be recognised, each imposing its own regimes of spatial organisation. Programming a few vignettes illustrates, as here, these representational paradigms, which comprise some of the basic data structures encountered by any programming architect, and some of the general, underlying forms of organising and performing space in a computer.

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Perhaps the most basic form of spatial data is a simple sequence of values stored contiguously in memory as an array, where the spatial relation is one of adjacency between data, as if we would consider the tape of the Turing machine literally as a space. Considering lengths of this tape cut and adjacent to each other, it is possible to build square or cubic lattices or matrices, the neighbours of each element easily accessible by its position in the sequence. This is not only the standard form of representing raster image data, but also of representing space in cellular automata, for example. Independent of the algorithm we use, or of the dimensions we operate with, space as an array implies its discretisation into cells, their arrangement into a lattice and the association of some quantity (the data) to that spatial arrangement.

Another basic form of representing space is as a geometrical location through Cartesian coordinates. But a set of geometrical points conveys no structural information, as the lattice in an array does. This needs to come either from their order and arrangement, in pairs to form line segments, or in sequences to form polygonal lines, or it may be calculated as part of the algorithm, as in the case of a swarm, in which proximity relations between particle locations are calculated at each iteration of the algorithm, the structure of adjacencies mutating at each step.

Often structural relations between elements are encoded as graphs; their basis is the representation of relations between these elements, called nodes or vertices, through pair-wise connections known as edges, arcs or links. The basic information of a graph is not so much its specific links as its overall structure and organisation, as can be seen in the examples of the spatial networks of the Bronze Age fortification of Tiryns or the street networks in the town of Apple Valley, Minnesota. Besides representing networks, graphs such as polygon meshes and unstructured grids are also common forms of describing geometry in the computer. Meshes are graphs with added constraints so they can efficiently represent polygonal faces. However, common mesh data structures also impose limitations on the topology of the surfaces they can represent, particularly in the difficulty of describing non-manifolds. The effects of this in architecture are not trivial, as this limitation is strongly linked to the emphasis on surfaces and envelope of current computational design, particularly through the use of mesh modelling techniques such as those available in Autodesk Maya or Blender.

Pablo Miranda Carranza, Swarm algorithm with 1,000 particles, KTH Royal Institute of Technology, Stockholm, 2014At each iteration of the algorithm, new positions are calculated for each particle. Particles also have velocity, which determines their future position. This velocity is a weighted sum of the velocities and positions of the closest neighbours of each particle.

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Pablo Miranda Carranza, Subdivision surface, KTH Royal Institute of Technology, Stockholm, 2014below top: Eight iterations of the Loop subdivision scheme applied to an icosahedron, adding random noise to the position of each mesh vertex at each iteration. This Loop subdivision scheme is part of the Open Source CGAL Polyhedral surface library.

Pablo Miranda Carranza, Closeness centrality of the Bronze Age fortress of Tiryns, Peloponnese, Greece, KTH Royal Institute of Technology, Stockholm, 2014bottom right: The size of the circles and the text labels show the closeness centrality for the spaces of Tiryns. Closeness centrality was proposed by sociologist Linton Freeman in 1979 as a measure of centrality in the analysis of social networks. It is also fundamental in space syntax analysis. Calculated using the Open Source Boost graph library.Pablo Miranda Carranza,

Betweenness centrality of Apple Valley, Minnesota, KTH Royal Institute of Technology, Stockholm, 2014bottom left: The width of the roads shows their betweenness centrality, another measure used in network analysis. It is calculated by counting the amount of shortest paths that pass through an edge or node, for all shortest paths from every node to all other nodes. Calculated using the Open Source Boost graph library.

Programs as ArchitectureWhile everyday environments are largely dependent on the control programs of climatic and lighting systems, elevators and access cards, and in general on all the informational gadgetry that makes up contemporary daily life, this programming of the environment is only marginally addressed in architecture, as its traditional means of representation, drawings and geometry can hardly account for it. Th e following two examples use programs to aff ect space, rather than as a way of representing it. SplineGraft, developed with Jonas Runberger as part of the architecture research group Krets, consists of a number of microcontrollers connected wirelessly, each modulating, through a set of muscle-wire actuators, the shape of a rectangular foam surface. Using a genetic algorithm, the installation tries to evolve movement patterns that promote the occupation of the area facing the installation. In the second example, the interaction and electronics of Spoorg, created with smund Izaki for the design collaborative servo, 18 Atmel AVR microcontrollers generate sound responses to the movements of visitors. Similarly to how birds evolve and learn mating songs, each microcontroller wirelessly broadcasts its response pattern, which its neighbours then recombine with their own response schemes.

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Notes1. Colin Rowe, Program vs Paradigm, Cornell Journal of Architecture, 2, 1983, pp 919.2. Reyner Banham, Theory and Design in the First Machine Age, Architectural Press (London), 1960, p 212.3. Michel Foucault, The Archaeology of Knowledge, Tavistock Publications (London), 1972, p 30.4. Thomas H Cormen, Charles E Leiserson, Ronald L Rivest and Clifford

Stein, Introduction to Algorithms, 3rd edn, MIT Press (Cambridge, MA), 2009, p 10.5. Donald E Knuth, The Art of Computer Programming Volume 1: Fundamental Algorithms, 2nd edn, Addison-Wesley (Reading, MA), 1973, p 9.6. Ibid, p 225.7. Ibid, p 228.8. Ibid, p 9.

Text 2014 John Wiley & Sons Ltd. Images: pp 66-72, 73(l) Pablo Miranda Carranza; p 73(br) Jonas Runberger and Pablo Miranda Carranza; p 73(tr) Image Courtesy of the MAK Center, photography by Joshua White/JWPictures.com

servo with smund Izaki and Pablo Miranda Carranza, Spoorg, Schindler House, MAK Center, Los Angeles, 20067 below left: Diagram of the interaction and electronic infrastructure of Spoorg showing the radio broadcasting and interaction logic between the microcontrollers.

Pablo Miranda Carranza and Jonas Runberger/Krets, SplineGraft, Zeche Zollverein, Essen, Germany, 2006bottom right: Exhibited at Open House: Architecture and Technology for Intelligent Living, SplineGraft consists of a series of microcontrollers each managing 10 shape memory alloy actuators. Every two hours a steady-state genetic algorithm generates new movement patterns, and their effect on the behaviour of visitors is measured through an infrared motion sensor. The installation tries to evolve over the exhibition period patterns of movement that encourage visitor presence in front of it.

below right: Designed by servo, with interaction design by smund Izaki and Pablo Miranda Carranza, 18 microcontrollers generate sound responses to the movements of visitors, which, after evaluation, they broadcast to their neighbours; these recombine the received response patterns with their own. Eventually, the group of microcontrollers evolves sound responses that promote visitor interaction.

Both SplineGraft and Spoorg relate in the way they are arranged to the data structures outlined above for the representation of space in software: SplineGraft is analogous to an array, as each microcontroller and its rack of actuators, laid out parallel to each other, cover a rectangular surface; and Spoorgs spatial strategy is close to the organisation of a swarm, in which each element develops ad-hoc, temporary interactions with its neighbours. But besides these parallels, these two projects exemplify existing approaches in architecture that treat programs, algorithms and electronic infrastructures as architectural materials, rather than as its means of representation. Thus, in addition to the types and diagrams mediating architectures representation through computers, it is interesting to consider the paradigms governing this use of computer programs as architectural material. After all, indicator lamps, gauges, buttons, beeps, automatic doors and water taps, digital displays, temperature, light, humidity and movement sensors or RFID tags, together with the software controlling them, are already part of a vernacular of interactive architecture increasingly defining our daily environments. 1

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