On the Search for Spatial Patterns: Repetition as the Crystallization of a Design Method


Essay by Clara Olóriz Sanjuán.


The machine can only be understood as a tool that continuously repeats a predetermined cycle of activity, becoming economical as the result of producing a large number of identical parts. . . . It is the source of all the consequences, by which the industrial process is determined.1
—Konrad Wachsmann, The Turning Point of Building, 1961

In the 1950s and 60s a group of Spanish architects embodied the “turning point” in the architectural profession—envisioned by Konrad Wachsmann—from their own local understanding. Among them were Rafael Leoz, Alejandro de la Sota, and Emilio Pérez Piñero. The clarity of their expression and uncompromised use of technology stemmed the creation of three remarkable production systems: the collapsible rod’s bundle by Emilio Perez Piñero from 1965, the Horpresa system by Julio Garrido in Alejandro de la Sota’s residence-school from 1967, and the HELE module by Rafael Leoz and Joaquín Hervás from 1960. While they are very different, they piece together an argument that responds to the condition of repetition in the form of a grid. Each of them inhabits this spatial pattern under a particular scalar understanding that is contained in the notion of system: from the mechanics of the parts in Perez Piñero, to the ruled paper to which De la Sota entrusted the materialization of the ideas, to the possibilities of endless reproduction contained in Leoz’s totality. Repetition is thus the condition that binds together all these scales in a very particular form that these three architects share, one that is found in nature. From these premises, repetition will be tackled here not as a result or consequence but as a condition or action; an operation under the guidance of a methodology carefully choreographed by the system that poses several questions: What is implied in the act of repetition? What is the understanding of space in the production of multiplicity? How is space produced and actualized?

Perez Piñero’s collapsible structure patent is described as a “system of rods pivotally connected to each other by couplings which can be distributed by unfolding over a three-dimensional space and be folded until the rods and their coupling connections form a compact bundle which is easily manageable.”2 This structural system was used in the itinerant theatre proposal in 1961, in a dismountable pavilion for exhibitions in 1964 that travelled from Madrid, to Barcelona, and San Sebastian to commemorate 25 years of peace since the Spanish Civil War, in a lunar module, a collapsible structure for great-span domes and the unfoldable stained-glass window that he designed with Dalí.

The collapsible set of rigid rods that form a bundle was considered by Piñero as a “mechanism” which does not become a rigid structure until the ends are connected to the cables that complete the triangulation of the structure. The component was conceived as a structural member similar to a row of collapsible chairs assembled together. It is formed by a central coupling and is assembled to the adjacent components at each of the ends with other couplings, thus, each rod is anchored in one upper, lower, and intermediate coupling. The end couplings are tied by tension cables to restrict the opening and avoid the closing of the bundles once it is mounted. The upper layer of cables could be substituted for a fabric or a covering material to build a roof. In Perez Piñero’s words, the material structure parallels the behavior of a vertebrate body, the rods representing the skeleton in compression that channels the forces, and the tension cables being an analogy of the muscular system that surrounds and maintains the skeleton as a living structure.3 The component represented, in the rationalist sense of structure, the material skeleton that channeled the forces.

Perez Piñero’s formal understanding resembles the part-to-part and part-to-whole relationships of the micro-form and macro-form found in crystals, inspired by the ideas of French architect and engineer Robert Le Ricolais. Along these lines, he compares architecture with music with regards to their essential structure and combinatorial laws based on mathematics, geometry, or mechanics.4 The aggregation of the bundles generates the macro-form that spans the space by the unfolding of the components that are fixed by means of cables. The micro-form or inner structural definition of the component, that is to say, the variations in the number of rods and the location of the bundle’s joint affects the organization and pattern of the system:

Equality or inequality of distances between each intermediate coupling and the two other extreme couplings of each rod. If the intermediate coupling is equidistant from the two other extreme ones (i.e. the upper and lower), the extended structure does not present any curvature. . . . If the intermediate coupling is not equidistant from the other two, then the extended structure adopts the form of a curve (a shell-shaped configuration); that is to say that the couplings of the same designation are found upon one of its three curved surfaces, concave towards the interior of the covered enclosure.5

Thus, the structural system conceived by Perez Piñero as a pattern of bundles of rods is both a mechanical structure but also a structural configuration.6 As a structural configuration, the way the structural parts or rod’s bundles are assembled or the way elemental material is distributed and organized in space determines the properties of the structure.7 Form is dealt here at two different scales: “macro-form” or extended structure which responds to the anti-funicular of the loads and the “micro-form” as the internal structure that channels the efforts, the local form of distribution or the assembly of the parts. The way material is arranged in the space is considered by Piñero as determinant of the micro-form, paralleling the microstructure of crystals or the ordered pattern of atoms and molecules. He considered form as “resistant form” and “material form”8 in which he highlighted respectively the identification of the conjunction form-structure as generator of resistance in the macroform and the indissoluble dualism form-matter in the micro-form or intermolecular forces and of course, their interrelation.9

The idea of crystalline meshes can also be found in his definition of historical archetypes as the crystalline conjunction between matter, structure, and form. This conjunction provides the classificatory potential to structure as in the vegetal and animal classifications: the structural morphology. He compares this approach towards form with the mineral crystals whose distinctiveness resides in the system in which they crystalize, that is to say the process through which their internal structure is formed.

Crystalizing patterns are also implicit in the use of the Horpresa system and building method by Alejandro de la Sota in his unbuilt project for a school-residence in Orense from 1967. The patent of these panels was designed by Julio Garrido and consists of a multiple-position, hollowed, pre-stressed concrete panel that can serve as an element for the construction of walls, slabs, facades, and roofs. Its geometrical definition consists of a box beam with ribbed ends in C-shape. The exterior plain faces are parallel to each other and the interior hollow has a rectangular shape with eight sides. Julio Garrido set the dimensions of the panels in a series of 16, 17, 18, and 20 cm for the width, and for the other two dimensions: one is fixed to 43 cm, and the other—the span—is open to variation. The set of dimensions of the elements offers variation to be adapted and assembled in various positions. Moreover, by pouring concrete in to the joints, a monolithic structure either for a slab or a wall can be obtained.

In an interview with architect Mariano Bayón, he recalled de la Sota being very worried because he had been working on this project for three years, the client was coming to visit him, and he had only one plan:

“It is graph paper! And of course here there is everything,” exclaims Bayón. This graph paper contains everything—structural plans, prefabricated walls, even installations—and moreover it reflects the new modes of “projecting with the system.” Thus, beyond the multiple positions in which the panel can be placed, the gridded paper is also the instrument with which the system lays down the guidelines or norms for the production of, or “to project,” architecture. Since it is a prefabricated system, everything is ruled. It is unified under the systemic laws. According to Bayón, de la Sota used to tell them “there are some form of crystalline meshes that are not visible and architecture reveals them.” He describes these meshes as a stereotomy—the geometry of cutting and assembling stones—inherent to space and the role of the architect is to unveil them; the role of architecture is to actualize them through the crystallographic twinnings or macles. These crystals develop under certain organizing rhythms, graticules, or grids providing with complete solutions, everything is contained in the panel system. De la Sota’s graph paper shows not only the way he operates with the repeated components but also his spatial conception and architecture’s role within it. Similarly, Fuller defines this process of actualization as the organization of “the assemblage of visible structures out of subvisible modular structures,” the macro and micro-form.10

Rafael Leoz’s investigation focused on the search of “subvisible modular structures” to find homogenous and systemic divisions of space. One of the most interesting aspects of his methodology is the reversal of the order of the usual procedures in prefabricated methods, which start from construction details to arrive at a general solution. In these terms, repetition is tackled from the overall perspective of the spatial studies to give a response, subsequently, to the specific problem. Searching for more general laws towards the industrialization of building evades the lingering on anecdotic details from the very beginning. Most of the preceding experiments to cope with industrialization conditionings departed from a very sophisticated construction detail hoping to produce architecture from a technical detail, as a fundamental element. Alternatively, the priority here is in the essence of the architectonic space and its inherent structure and configuration.11 Thus, he starts from the very organization and structuring of space: “the division and organization of architectonic space”12 or “the harmonic systematization of space.”13

This approach can be related to Reyner Banham’s description of the Crystal Palace from 1851 that symbolizes repetition as precondition for the industrial revolution. The British critique foresaw in “the repetitive glass and iron units” a space which “seemed to contain infinity within itself,. . . . running off endlessly as far as the eye could see,” and what is more, space was “measured off by the regular module of the structure till it flickered away in an optical haze compounded on distance and light.”14 It is as if, rather than space being produced by the sum or repetition of units, space was produced through the subdivision of its infiniteness, through its infinite measurement.

Twenty-five years after the Crystal Palace was built, Viollet-le-Duc, inspired by the thirteenth-century French architecture, defines form “simply as the result of structural combinations; geometry bears away the palm from painting” and as “the result of reasoning and calculation.”15 This statement defines industrialized architectural tools and production methods: “structural combinations” and “geometry,” combining and measuring instruments which conditioned architects’ modes of operation, in the application of mass-production techniques inherited from World War II. Even the notion of geometry and mathematics itself, influenced by scientific advances, would be deeply transformed. In 1953, the MIT’s department of mathematics defined “mathematics” as what “most people think of as the science of number, is, in fact, the science of STRUCTURE and PATTERN in general.”16

Geometry is thereafter the instrument that materializes the necessary linkage between industrial production and architects’ design processes, constructing their common ground. Along these lines, Leoz describes the departure point of his studies and the architects’ tool as: logic, pure mathematics and within it, geometry and combinatorial topology.17 Leoz intended to find a methodology or system to cope with the housing shortage with more efficient, accurate and fast techniques. He envisioned the establishment of an open system with which architects could operate with the maximum flexibility and the most rigorous geometrical organization.

The design methodology departs from the abstract organization of space, continuing with the determination of the dimensions, scale and modular coordination to arrive at the production of the components and their assembly, as the matter that is arranged in the systematization of space. His inquiries were initiated by the homogenous division of the three-dimensional Cartesian space by means of infinite series of spheres; then, it evolved towards the study of the four polyhedrons of radial symmetry fit to be inscribed in a sphere and to solidify space—the cube or regular hexahedron, the regular hexagonal prism, rhomb-dodecahedron, truncated octahedron (tetra-decahedron), or Lord Kelvin’s polyhedron—generating four spatial systematized networks, suitable to undergo affine transformations. Furthermore, Leoz intersected these assemblies of spheres and polyhedrons with planes passing through their centers that resulted in regular unlimited networks. These planar parallel sections, obtained from the spatial networks, originated planar grids that enabled the materialization of these simplified patterns by industry. These planar networks also corresponded to three planar right-angled triangles: the 45-45-90 triangle, the 30-60-90 triangle and the hemi-Pythagorean triangle—half of a Pythagorean triangle, an isosceles triangle in which the base is equal to the height.

Once space has been systematized through these patterns, more complex geometries can be achieved through their infinite affine transformations and their potential third dimension. Leoz devises four, six, or seven parallelograms or atoms for each organization respectively, formed by four equi-superficial triangles or quanta. The subsequent combination of these atoms generates a molecule that responds to the HELE rhythm or combinatorial law: an ordered L-movement within the spatial networks in their “chemically pure state.”18 These molecular compounds have the potential to be endlessly combined, thus, Leoz proposes to evolve from the general basic unit into a more complex topological multiplicity of operations in the generation of forms. He names this methodology as “geometric gene” or lawful combination of empty and full components, enabled by attributing a polyhedral structure to organize space in an isotropic and homogenous manner.19

Le Corbusier referred to Leoz’s work as an analogy with language, chemistry, genetics, and music, all of them sharing the lawful combination of a limited number of components into highly complex results.20 Similarly, Leoz claimed that architects were confronted with very few components to prefabricate an infinity of results suitable to be combined between themselves. He compared the terrestrial material creation, result of the combination of a hundred different primary chemical elements, with his method of architectonic industrial prefabrication.21 The combination of HELE molecules—similar to crystals’ molecules or atoms that are arranged in three-dimensional patterns—encompassed an ordering, homogeneous, and unifying understanding of space “measured off” by spatial frames. Structure is thus the only form that can be assigned to space; moreover, every idea about space is already a potential structure,22 thus, a reading or production of space as structural patterns; an understanding of the wholeness and “modular nature” of the world as Morrison puts it:

“The whole even of our world—radiant energy and protein matter, crystals and cells, stars and atoms—share the modular nature. . . . The prodigality of the world is only a prodigality of combination, a richness beyond human grasp contained in the interacting multiplicity of a few modules, but modules which nature has made in very hosts.”23

These three projects tackle repetition by means of the natural analogy of crystal patterns, their intermolecular forces, processes of crystallization, modular nature, and wholeness. The crystalline paradigm is intrinsically related to the construction of space as a potential ordering structure that embodies the laws of generation and the parts as a totality. Space is produced through the lawful geometrical subdivision that rules the combination of molecular rhythms. As seen in de la Sota’s graph paper, it contains everything and becomes an underlying unity or unified whole; a whole that is open because “a minimum of substance produces a maximum law;” homogenous because it is ruled and infinite since it can endlessly grow in the limitless subdivision of space.24 As a condition of the production system and instrumentalized by the graph paper, these spatial patterns affect and regulate the way designers operate and “project” with it. Moreover, they affect the architectural production and its formation processes which are defined as the actualization of crystalline twinings or conjunctions of intermolecular forces.

The previous examples inhabit and give form to a gridded space, one that has the following characteristics: homogenous order, systematic parts, lawful combination, and overall structure. It is a grid that materializes through a specific act: crystallization and one that fuses mechanics and structural arrangements. Throughout the three examples, the act of repetition becomes a method that embodies the component or part in Perez Piñero, the rules or guidelines in de la Sota’s graph paper and the totality in Leoz’s infinite subdivisions.

These approaches towards architectural production relate to their contemporary discourses about the understanding of “atomism versus form” and the morphological relationship between structure and form which were developed in concrete art and reflected in texts such as György Kepes’ Structure in Art and in Science or Lancelot Law Whyte’s Aspects of Form. Deeply influenced by the scientific discoveries about matter, form, and structure, they devised “a shift of emphasis from two contrasted ideas: from relatively isolated small units and over-all shapes, towards a single comprehensive and precise identification of structural patterns and their changes.”25 These modes of architectural production and thinking have in common the crystalline analogy in which “the pieces have lost (or almost lost) their own meaning, and the structural or logical pattern is in complete command.”26 Or, as Lohse poses it:

An essential prerequisite for this advance was the recognition of the necessity of neutralizing the media; the element is defined as an anonymous form. . . . It is recognized in the course of the working process that the objectified element can only be operative in the community, as a member of a group, or in other words the anonymous, the objectified, the singular has the ability to operate only with other identical individuals. A minimum of substance thus produces a maximum of law, from which it follows that new picture structures can only be realized if it proves possible to convert the principle of addition of the identical into one mobile law governed regularity.27

The resulting spatial understanding in their work is conditioned or rather produced by the logics of addition in the implementation of industrialized methods of production. Through the manufacture of large quantities of identical components, these systems transform the status of the architectural object, its production processes and, above all, the way architects operate. The fundamental requisite for these systems to succeed is the repeatability of their components, entailing a common modular coordination between design, production, and assembly and determining the geometrical definition of the parts. The establishment of geometrical laws or abstract system of dimensions allows the systematization of the media and the construction of a comprehensive methodology. The potential aggregation of the component is enabled by a new understanding of spatial patterns and rhythms that encompasses a new cosmology, or a new conception of the laws and structure of the “architectural” universe.

The production of space as potential ruling structures responds to the prerequisite mentioned by Lohse in the previous quote: “the recognition of the necessity of neutralizing the media.” The synthetic, common efforts, departure points, and homogenous work are proposed by de la Sota’s prefabrication methods as a critique to architect’s individuality or Whyte’s isolated and overall shapes.28 The grid becomes the precondition, instrument, and requirement sine qua non for the establishment of a common method, a common industrial language materialized in the graph paper. The structural pattern acts as a framework, as “the basis for the wholeness of the appearance, of their formations and transformations”29 or as “an aspect of the morphologic process”30 within which architecture is actualized and architects operate with maximum flexibility and “minimum substance.” The gridded paper becomes the site to search for spatial patterns as the framework where the repetition of fundamental components will take place.

The system or methodology constructs a “governed regularity” in which the mesh reifies the set of instructions or laws, as the homogenizing base. The three examples here discussed were conditioned by the establishment of a common system for which the systematization of space is an inescapable prerequisite; it is the basis for the common understanding of the agencies involved. This grid is not new to the industrial methodologies; it has been only instrumentalized by them. In one way or another, it has been present in previous architectural manuals and academic attempts to systematize design by establishing common and scientific methodologies. This is a tradition within the discipline that continues developing in the efforts to institutionalize or validate certain styles, modes of work, theories and approaches in the form of unifying or all-encompassing “methodologies.”

Practices related to types, that use the part-to-part or part-to-whole relationships to understand the city or to produce it, looking for generic aspects that make possible comprehensive classifications; the infinite iterations or variations of digital and algorithmic design that are deployed within a spatial mesh or even biological analogies that simulate natural structures are usually related to contemporary forms of production and use these methods to validate design decisions. Supposedly, new technologies of production have overcome the repetition of Wachsmann´s “predetermined cycle of activity” however, structural meshes and lawful methods are still pertinent to the discipline as an operative instrument to establish comprehensive practices. This makes us interrogate the implicit reductionism of methods and wonder whether this critical condition is still truly inescapable; whether architects or designers can only operate and take decisions under the frame, guidance and validation of a method. If the answer is yes, then, the question becomes: how do we overcome the totalitarian aspirations of gridded methods?

1 Konrad Wachsmann, The Turning Point of Building: Structure and Design (New York: Reinhold Publishing Corporation, 1961), 49.
2 Emilio Perez Piñero, Patent CA707069A ‘Folding three-dimensional reticular structure’ 06.04.1965, viewed March 2011,
3 ‘Su forma de trabajo se asemeja al cuerpo de un vertebrado. Las barras a compresión forman un esqueleto, una auténtica columna vertebral. Las barras de rigidación actúan como el sistema muscular que envuelve y mantiene el esqueleto. . . . El cedimiento o movimiento de un apoyo produce, asimismo una readaptación de trabajo en la estructura. Es sencillamente una estructura viva.’ Emilio Perez Piñero, ‘Estructuras Reticulares Tridimensionales’ Arquitectura 112 (April 1968): 4.
4 Emilio Perez Piñero. ‘Materia, Estructura, Forma’ Hogar y Arquitectura 40 (May-June 1962): 25.
5 Perez Peñero, Patent CA707069A.
6 As Adrian Forty remarks in his chapter about Structure in Words and Buildings, in architecture structure as mechanical support has never seen superseded by subsequent evolutions of the term because Structure in the rationalist sense or as the biological metaphor, permitted architects to claim a certain privilege and because of the physical nature of part of the architectural production. Adrian Forty, ‘Structure,’ Words and Buildings: A Vocabulary of Modern Architecture, (London: Thames & Hudson, 2000), 283.
7 No sólo han sido los materiales empleados lo que ha permitido ampliar estos espacios, sino que fundamentalmente ha sido el concepto mecánico, que ha manejado estos materiales determinando la forma de la estructura sustentante considerada como un todo (macroforma) y la forma local de distribución y ensamble de las porciones elementales de material que la constituyen (microforma).’ Emilio Perez Piñero, ‘Notas sobre las estructuras’ Arquitectura 66 (June 1964), 22.
8 Churtichaga classified in ‘La Estructura Veloz. Trayectorias Estructurales a Propósito de la Obra De Emilio Perez Piñero y Felix Candela.’
9 ‘La determinación de la retícula interna, o ‘micro-forma’, debe estar inspirada, como ya hemos dicho, en las trayectorias de tensión que en la forma general, o ‘macro-forma’, produzca el sistema de cargas exteriores.’ Perez Piñero, ‘Estructuras Reticulares Tridimensionales,’ 2.
10 Buckminster Fuller, ‘Conceptuality of Fundamental Structures’ Structure in Art and in Science, ed. Gyorgy Kepes (London: Studio Vista, 1965), 68.
11 ‘Insistimos en que lo primero es conocer la esencia del espacio arquitectónico y su íntima estructura y configuración a través de investigaciones puras, de análisis y síntesis de sus detalles y de su esencia.’
‘Parten de un detalle constructivo hecho con cierto material y generalmente bien realizado. A partir de ese detalle, y como elemento fundamental, se pretende hacer arquitectura.’ Rafael Leoz, ‘Sistematización armónica del espacio arquitectónico hacia la industrialización’ Arquitectura 111 (February), 30.
‘Lo importante son las leyes generales, porque las soluciones concretas y singulares no son más que una anécdota dentro del sistema. Todas esas soluciones no son otra cosa que variaciones sobre el mismo tema.’ Rafael Leoz, Redes y Ritmos Espaciales (Madrid: Blume, 1969), 143.
An alternative argument to Leoz’s hierarchy can be found in Wachsmann: ‘The dissociation of large and very large volumes into small and very small individual parts, which may represent either positive objects or the single negative moulds used in creating large, homogeneous structures, means that the starting point for structural conceptions must be the cell or unit element.’ Wachsmann, The Turning Point of Building, 232.
12 Rafael Leoz, ‘División y organización del espacio arquitectónico’ Arquitectura 89 (April 1966), 27.
13 Rafael Leoz, ‘Sistematización armónica del espacio arquitectónico hacia la industrialización’ Arquitectura 111 (February 1968), 30.
14 Reyner Banham, Guide to Modern Architecture (London: Architectural Press, 1962), 50-51.
15 Eugène-Emmanuel Viollet-Le-Duc, Discourses on Architecture (London: George Allen & Unwin, 1959), 249.
16 Buckminster Fuller, ‘Conceptuality of Fundamental Structures,’ 68.
17 ‘Los estudios propios del arquitecto en sus más altos estratos son: la lógica, la matemática pura y, dentro de ella, la geometría y la topología combinatoria, la coordinación modular, los estudios sobre el ‘hábitat humano’, las dimensiones óptimas de los nuevos materiales dentro de las nuevas técnicas, etc.’ Leoz, Redes y Ritmos Espaciales, 46.
18 Rafael Leoz proposed this ‘chemically pure’ state in order to arrive at the indispensable linkage between geometry and industry for the systematization of the architectonic design. Arquitectura e Industrialización de la Construcción/ Architecture and Industrialised Building (Madrid: Fundación Rafael Leoz para la Investigación y Promoción de la Arquitectura Social, 1981), 31.
19 ‘Esta genética geométrica parte del estudio sistematizado del espacio arquitectónico, adjudicándole a éste una estructura poliédrica de organización isotrópica y homogénea, donde los vacíos y los llenos participan de las mismas leyes, a partir de las cuales se generan las combinaciones necesarias y a las que se les puede dotar de toda la intencionalidad expresiva que el proyectista desee’ Rafael Leoz, Fundación Rafael Leoz (Madrid: Fundación Rafael Leoz para la Investigación y Promoción de la Arquitectura Social, 1981).
20 Le Corbusier, Arquitectura e Industrialización de la Construcción, 44.
21 Leoz, Redes y Ritmos Espaciales, 44.
22 ‘La estructura es la única forma que se puede asignar al espacio; más aún, toda idea de espacio es ya en potencia una estructura.’ Leoz, Redes y Ritmos Espaciales, 45.
23 Philip Morrison, ‘The Modularity of Knowing’ Module, Proportion, Symmetry, Rhythm, ed. Gyorgy Kepes (New York: Studio George Braziller, 1966), 1.
24 Richard Paul Lohse, “Lines of Development 1943-1984” Modular and Serial Orders (Waser Verlag, 1984), 136.
25 Lancelot Law Whyte, ‘Atomism Structure and Form’ Structure in Art and in Science, ed. Gyorgy Kepes (London: Studio Vista, 1965), 20.
26 Jacob Bronowski, ‘The Discovery of Form’ Structure in Art and in Science, ed. Gyorgy Kepes (London: Studio Vista, 1965), 59.
27 Richard Paul Lohse, ‘Modular Orders’ Modular and Serial Orders(Waser Verlag, 1984), 156.
28 Alejandro de la Sota, ‘Sentimiento Arquitectónico de la Prefabricación’ Arquitectura 111 (February 1968), 12.
29 ‘In morphology, i.e., in the doctrine of forms, structure is treated generally as the basis for the wholeness of the appearance, of their formations and transformations; one can also say, as their prerequisite.’ Margaret Staber, ‘Concrete Painting as Structural Painting’ Structure in Art and in Science, ed. Gyorgy Kepes (London: Studio Vista, 1965), 184.
30 Quoting from Whyte: ‘. . . . not a rigid scaffolding for a schematized reality, but an aspect of the morphologic process.’ Gyorgy Kepes, Introduction to Structure in Art and in Science (London: Studio Vista, 1965), iv.