Symmetry-Based Generative Design : A Teaching Experiment

2006

The relationship between geometry and architectural design are described and discussed along some examples. Geometry is the fundamental science of forms and their order. Geometric figures, forms and transformations build the material of architectural design. In the history of architecture geometric rules based on the ideas of proportions and symmetries formed fixed tools for architectural design. Proportions were analyzed in nature and found as general aesthetic categories across nature and art. Therefore proportions such as the golden section were seen as the power to create harmony in architecture as well as in art and music. According Pythagoras there were general principles for harmony. They were also applied in architecture and they found a further development especially in the renaissance. Leon Battista Alberti integrated such general harmonic proportion rules in his theory of architecture and realized them in his buildings. To find general principles of harmony in the world w...

Structural thinking in architecture is based on structuring information with the help of mathematical-geometric methods. Some of those methods are presented in this paper which had been one of the background for the DAAD Summer School "Structure – sculpture" in Buenos Aires, where students worked on the design task analyzing and redesigning the Ulm Pavilion by Max Bill. An overview of several mathematical-geometric approaches will be given accompanied by examples of teaching practice at Ulm School of Design in Germany, an innovative international school experiment between 1953 and 1968, where those methods had an important impact.

The concept of symmetry has been usually restricted to bilateral symmetry, though in an extended sense it refers to any isometric transformation that maintains a certain shape invariant. Groups of operations such as translation, rotation, reflection and combinations of these originate patterns classified by modern mathematics as point groups, friezes and wallpapers (March and Steadman, 1974). This extended notion represents a tool for the recognition and reproduction of patterns, a primal aspect of the perception, comprehension and description of everything that we see. Another aspect of this process is the perception of shapes, primary and emergent. Primary shapes are the ones explicitly represented and emergent shapes are the ones implicit in the others (Gero and Yan, 1994). Some groups of shapes known as Semantic Shapes are especially meaningful in architecture, expressing visual features so as symmetry, rhythm, movement and balance. The extended understanding of the concept of s...

… Association of Societies of Design Research …, 2007

This paper identifies various geometric concepts, principles and constructions which are of great value to design researchers and practitioners. Particular attention is focused on geometric symmetry as the basis of an analytical tool to examine designs in different cultural or historical contexts. Relevant empirical literature is identified. Illustrations of regularly repeating designs are presented; these result from the application of a system of pattern construction, based on taking components of certain regular polygons and applying various symmetry operations.

Katona, V. (2018) Symmetries and Proportions in Architecture. Symmetry: Culture and Science, vol. 29, no. 3, pp. 325–327., 2018

On 18 August 1418, the Florentine Arte della Lana announced an architectural competition for building the dome of Santa Maria del Fiore Cathedral using Neri di Fioravanti's design. The two main competitors were two master goldsmiths, Lorenzo Ghiberti (by whom the concept of symmetry was first explained in vulgar Italian) and Filippo Brunelleschi. Lifelong competition between the two remained sharp, but Brunelleschi received the commission, and completed the dome in 1436. It was the first "octagonal" dome in history to be built without a temporary wooden supporting frame, and was one of the most impressive projects of its time.

Periodica Polytechnica Architecture, 2023

The tessellation method, which is a mathematical concept used in geometric design, is also used in architecture and engineering, as in many other fields. In this study, it is aimed to investigate the tessellation configurations in structural systems within the scope of geometric design in architecture, to show the effectiveness of geometry in the architectural production in these structures and to highlight the tessellation-structure relationship. The number of studies emphasizing tessellation configurations in structural systems is limited. For this reason, the study will contribute to the literature. The research question of the study is how tessellation configurations are applied in structural systems and how this relationship is established. Depending on this research question, eight architectural buildings in different cities with different tessellation configurations were examined within the scope of this study. Content analysis was performed by looking at the architectural features of these structures, and a comparative analysis framework was created with the data obtained. Inferences were made on geometric and architectural features. As a result, it has been seen that tessellation patterns are used and will continue to be used on a wide scale in structural design.

riccardo.migliari.it

Descriptive geometry has a historically consolidated relationship with the art and the construction in general, and it could therefore not fail to be affected by the technological evolution we mentioned earlier. The classical corpus of texts on the discipline, based first of all on the representation methods, understood as the theories of the construction of the encoded image, appeared to be completely inadequate compared with the contemporary project procedure and, what is worse, it seemed unrelated to the new representation techniques of the space, while these last, at the same time, did not seem to have a basis theory of general character, but only the algorithms that permit to solve this or that particular problem. In the academic circles, the architects who, due to changing historical events, today are the repository of the discipline of descriptive geometry, have finally seized the wish for renewal that came above all from the youth, faced, on the one hand, with a theory that does not seem to have any more applications and, on the other, with a technique that is incomprehensible, precisely because it is lacking the general concepts of a theory; now, finally, is ongoing a process of revision and renewal of the classic descriptive geometry, which is based on new definitions of the fundamentals and fulfilled through integrations and transformations of the corpus of texts on the discipline. As we will see in a while, the integrations concern, essentially, the representation methods, while the transformations involve above all the construction procedures of the geometric shapes. The representation methods, in general, are distinguishable for two essential reasons: the first, and the most important, is that each of the methods is able to record the characteristics of the shape and the dimension of an object in the space and, at the same time, it is able to transfer the object back into the space once it has been represented. A method, to be considered as such, must be able to perform this path, in both directions, autonomously, that is, without turning to other methods. The second reason that permits to distinguish the methods, the one from the other, concerns the use of each of them within the planning activity: the metric control, as in the case of the representation in plan and elevation, or the formal and perceptual control, as in the case of the perspective. The information systems make use, basically, of two digital representation methods that have been called: mathematical representation and numerical or polygonal representation. The digital representation methods have some other extremely innovative characteristics, which have remarkable impacts on the planning as well as on the theoretical evolution of descriptive geometry and these are: the accuracy and the spatiality. This modality of the geometric expression, which uses the analogy to describe the result of a digital process, may appear to be hybrid, too, and not purely geometric. But, as a matter of fact, we are simply dealing with the fulfilment of one of Monge’s wishes, the synergies between analysis and synthesis, between symbolic languages and graphic languages, which the French mathematician already clearly expressed in the first edition of his most famous work (1798): the analytic geometry and descriptive geometry should be ‘cultivated’ together, since in this way the descriptive geometry would bring its own evidence into the most complex analytical processes and, in turn, the analysis would bring the generality and accuracy of the results to the descriptive geometry. After all, Monge’s idea has not been abandoned: this way of making research, open-minded, deliberately disrespectful of the fences that surround the disciplinary fields of mathematics, has illustrious supporters: from Guido Castelnuovo (1903) to Harold Scott Mc Donald Coxeter (1961). In former times, when electronic computers were still unknown or had far from reached their present-day world-wide distribution, the schools of mathematics have created a rich selection of three-dimensional models, maquettes in plaster, wood and other materials very similar to those which decorate the studio of an architect or a designer. Recently these collections have been subject to studies and additions carried out, precisely, with virtual models. René Thom (1977), while on the one hand he considers the descriptive geometry as an obsolete science, and affirms that he would like to free himself from the manipulation of the Euclidean three-dimensional bodies of the space, on the other hand he recognizes to the qualitative sciences the capability to construct models that are the only ones able to explain our surrounding world, even if they cannot give quantitative results. So, it really looks like as if the synergy hoped for by Monge, and today fully expressed by the union between the concise reasoning of the geometry and the electronic calculation, is able to create a synthesis between quantity and quality, producing results that, while they describe with audacious analogies and with great immediacy the reality of a phenomenon, they also allow a quantitative analysis with controlled accuracy.

2011

The present paper reports an ongoing investigation about morphogenetic patterns. It discusses latent potentials for controlling esthetical planar ornaments where algorithmic design processes play an important role in enhancing architectural design. Through the use of dynamic user-control and evolutionary processes, the algorithms introduced in this paper, embed freeform design out of planar components. This investigation is intended to extend the synthesis that computational geometry algorithms imply for the key stages of design knowledge. In order to optimize an intended design towards the fabrication strategy and the construction techniques, an early digital architectural design should integrate the following concepts: building shape, intended design, rational material and structural systems, digital fabrication methods and construction criteria [1,2]. The present paper focuses on explaining, through a series of ornamental experiments and related theory, the algorithmic potentiali...

Structure & Architecture, 2010

The design process presented here aimed at investigating the possibility of building geometrically complex architecture using simple techniques and very cheap materials, yet achieving a meaningful structural and architectural performance. Within an experimental workshop a team of 5 students supervised by the 2 authors built a real scale artefact, a temporary multi-religious pavilion with a tensile roof made of recycled cardboard.

Academia XXII, 2018

The aim of this paper is to describe some teaching procedures that have been applied in the education on structures for architecture students at the National Autonomous University of Mexico (unam). Even though most of the architecture curricula at Mexican higher education institutions include the subjects of mechanics and geometry, they are taught separately and are not applied to architectural concepts and structural design. In order to mitigate these undesirable teaching conditions, a group of professors has attempted to simultaneously incorporate mechanics and geometry into the conception and design of structures. In response to the aforementioned circumstances, 'Mechametry' was created as a new subject in the unam architecture curriculum. Mechametry has been offered for 10 years to undergraduate students, as well as to students in the Design of Lightweight Structures specialization course. Nowadays, many former students are working for companies in Mexico and around the world and are directly involved in the design and construction of shells and other spatial structures, primarily tensile surface structures. Some selected projects by these students will be shown and described in this paper, as will projects that have received awards in international contests for architecture students.

2018

The broad application of computational design and construction technologies has widely changed the use and perception of computer software in architecture. Thus, we have seen a shift from mere drawing-tools towards mighty parametric design methods. These tools have allowed many architects to form the conception and design of very complex architectural projects.

Geometry and Architecture, 2020

Architecture has its roots in geometry, which is drawn etymologically from “earth measuring”. Geometry was originally used for drawing ground plans in order to create bases for buildings. The Pythagorean theorem furnished us with a practical way to employ the right angle, the quintessence of architecture. However, despite its benefits during planning and construction, geometry, as an independent discipline, has its own rules and possibilities that facilitate morphologies free from the ties of gravity and matter. Starting from Platonic and Archimedean solids, architecture has been applying many of the free forms of a “celestial” geometry in order to reconnect them to the physical level.

Blucher Design Proceedings

Architecture has always relied on mathematics to achieve proportioned aesthetics, structural performance, and reasonable construction. Computational tools have now given architects the means to design and build spatial concepts that would have been inconceivable even ten years ago. Against this background the paper discusses an educational approach that focuses on the early integration of computational principles, regarding the definition of geometry as well as material and fabrication parameters to inform the architectural design. Three case studies illustrate the interdisciplinary approach, conceived and carried out jointly by the Department of Architecture and the Department of Mathematics.

31st ASME Design Automation Conference, 2005

An engineer presented with a design challenge often creates a symmetric solution. For instance, consider a table (front-back and left-right symmetry), a car (left and right symmetry), a bridge (front-back and left-right symmetry), or the space shuttle (left-right) symmetry. These examples may not be 100% symmetric, but their overriding features are remarkably similar. The reasons for the design of symmetric structures is not always clear. In some cases, like the table, symmetry may be a tradition. Similarly, the symmetry may be for aesthetic reasons. However in automated design algorithms, especially stochastic techniques, the output is often largely asymmetric. One reason for this is that fitness functions are not rewarded for symmetry. A possible resolution to this is to add a reward function for symmetry. Unfortunately, this approach is computationally intractable as well as arbitrary. In this paper a Genetic Algorithm based method is presented that rewards re-use of parts. The method is applied to a simple, idealized situation as well as to real design case. The results show that in some situations, symmetry naturally emerges from the synthesis, but that it does not provide clear performance advantages over asymmetric configurations.

CAADRIA proceedings

Nowadays the use of computational design processes in architecture is a common practice which is currently recovering a set of theories connected to computer science that were developed in the 60s and 70s. Such pioneering explorations were marked by an interest in employing scientific principles and methodologies many developed in Research Centres located in the US and the UK. Looking into this period, this paper investigates the relevance of the German design school of the Hochschule für Gestaltung (HfG) Ulm to the birth of computation in architecture. Even thought there were no computers in the school. It is argued that the innovative pedagogies and some distinct professors have launched clear foundations that can be understood as being at the basis of further computational approaches in architecture. By describing and relating the singular work by Tomas Maldonado (educational project), Max Bense (information aesthetics) and Horst Rittel (scientific methods), this paper describes the emergence of analogical ways of computational design thinking. This analysis ultimately wishes to contribute for inscribing the HfG Ulm at the cultural and technological mapping of computation in architecture.