The focus will be on scientific fields which areas of application use methodologies that stem from the mathematical sciences, especially those that have witnessed recent developments

 ontologies in architecture

The development of ontologies applicable to Architecture and Urbanism emerged from the necessity of finding common linguistic bases for the multiplicity of languages used by the numerous agents in the constructed environment. This is all the more necessary nowadays, as artificial agents are more and more present. These ontologies have been used as a nuclear language in knowledge-bases of constructed environments, as well as logical assistants to design, participatory GIS, automatic acquisition of urban knowledge, and interoperability between several data processing artificial agents (CAD’s, GIS, etc.).

Several digital tools, such as OWL, Protégé or KLOne, with their origin in information technologies, are being used to create ontologies on the architectural domain.

bim | vdc

BIM (Building Information Modelling) is an activity rather an object, is a human activity that involves logical thinking, digital entities and a large sort of specific software, with a strong impact in building design and construction activity. The transition to BIM, however, is not a natural progression from CAD (Computed Aided Design), because it involves a paradigm shift from “drawing” to “modelling”; a virtual model consisting of relationships between entities, organized into an object–based inheritance hierarchy. Technological and market trends are good predictors of the short–term future in this field, and it is opportune to analyze and discuss how BIM will be developed in different, yet correlated, aspects like VDC (Virtual Design to Construction) and the developments in peripheral hardware linked to building, prefabrication, assemblies, functions of construction management connected to ERP (Enterprise Resource Planning), ontological and semantic searching and compatibility of BEMs (Building Entity Models) to multiple platforms, IPD (Integrated Project Delivery), automated checking for code conformity and constructability to support Lean Construction, improved import and export capabilities using protocols like IFC (Industry Foundation Classes) and parametric 3D technical catalogues from manufacture industry, the setting up and development of National Building Standards in connection with Green Building, LEED (Leadership in Energy and Environmental Design) or Breeam (Building Research Establishment Environmental Assessment Methodology) and expanding the scope and discipline-specific BIM tools or even “light” BIM for specific building types like low cost residential houses, or small area building facilities.

CAM computer aided manufacturing

Advances in computation and its use to control production machines are being applied also to Architecture, allowing the automatic manufacture of complex geometries, hardly reachable in ancient techniques and at a fraction of the cost. Computer Aided Manufacturing and CNC (Computer Numerically Controlled) machines are enabling greater personalization, flexibility and innovation in architectural design and creative processes, providing society with new products and services.

Image courtesy of Vitruvius FabLab

cellular automata

´Cellular automata’ is a term used to refer to a set of generative grammars, where multiple agents exist with identical or differentiated rules that act concurrently in the built space. The concept of Cellular Automata structures itself in dynamic mathematical models, with the goal of configuring processes capable of promoting self-replication. Originally it explored a set of quadrangular elements on a grid where, following a set of rules of proximity relative to each cell (cellular automaton) along the grid, growth processes were simulated, based on the logic of complex systems. Cellular Automata established itself as a process that started with small elements following simple rules (bottom-up approaches). Research has been revealing a great potential in the fields of architecture and urbanism, as it allowed the possibility of creating dynamic patterns, through reciprocal interaction and conditions of neighbourhood between cells. They constitute patterns from which architectural and urban formal hypotheses may appear, following mathematical approaches free from traditional deterministic constraints. Usually they are implemented in digital tools for generic algebraic calculations or in parametric CAD applications.

gis geographic information systems

Since their emergence, in the 60’s of the 20th century, these territory analysis and planning digital tools - the Geographic Information Systems (GIS) - are evolving to adapt to the new and diffuse means in which territory is appropriated by the information based society. Together with the traditional interlacement of diverse layers of territorial information, the contemporary information practices of geo-spatialization almost allow their complete mapping on-line, dramatically reducing the gap between production and data visualization. Furthermore, the recent 3D presentations enable a friendly visualization of complex data, approaching the common citizen to urban participatory processes. The GIS experimentation field is nowadays exploring crossings with other tools of spatial analysis, such as space syntax. Other new emergent tools, as processing, will be able to connect to GIS in a near future.

parametric processes

Research on parametric processes has been tackling the evolution of different methods and technological processes, which lies in the possibility of quick visualization, construction, and modification of concepts associated with design. These systems establish a complementary relationship with generative design, where different parameters from several different components are intrinsically connected through an algorithm – in which the variables are then verified so as to be adjusted to the needs of specific results. From the initial analysis to the execution and production of final components, through the (no less important) phase of form-finding, parametric processes enable singular approaches to the set of conditions of each context. These conditions are formally framed via top-down strategies, or, conversely, using informal combinations of less structuring components as a way to promote results generated through bottom-up approaches.


Processing is a creative programming platform (IDE / Integrated Development Environment) supported by the Java language, which assumes the purpose of combining the different programming (and increasingly diverse) areas of digital arts, through structuring of visual media applications and interactive. Having had originally educational purpose - as a tool focused on teaching the graphical component that language, open source condition - quickly encouraged the participation of growing communities, increasing its development in areas such as performing arts, kinetic arts, data visualization interactive real-time experimental architecture, among other fields of artistic creation and applied research. Particularly in the architectural perspective, there is the in-depth research to the generative level design and implementation of limitations associated with "traditional" methods - where the Processing demonstrates its greatest potential, allowing the user (architect-developer) define specific dynamic applications that allow putting into practice the processing conditions and complex rules in creating certain architectural objects.

shape grammars

Shape grammars are technologies belonging to the broader field of generative grammars, dedicated to the production of geometric shapes. A shape grammar includes a generative algebra applied to a set of production rules. These grammars have been used in diverse areas, from technologies to the visual arts, as identifying styles of composition or as a means to refine structural elements. In architecture and urbanism this tool is used in history, theory, and critique (with examples like the definition of a grammar of Palladio's villas, or the formalization of Alberti’s production rules), as well as on automated design, based on rules defined by the architect, or according to rules or patterns identified from case studies or established practices.

space syntaxes

Space syntaxes consist of a set of theories and methodologies used for the study and treatment of building and urban space. Spaces can be geometrically defined through more or less abstract concepts: either geographic, (volumes, surfaces, axial lines, nodes), or topological (graphs and connections). These spatial elements establish simple relationships between themselves, like visibility or connectivity. It is possible to build a whole set of concepts based on this basic proprieties, which are usually quantifiable, like integration, depth or controllability.

These quantities represent architectural and urban realities, at a physical level (such as accessibility, connectivity), at the level of cognitive psychology (intelligibility, entropy) and of sociology (privacy, control, segregation). The space syntaxes have been extensively used on multiple fields of architectural analysis, especially at an urban scale, such as traffic studies, distribution of facilities or even the prediction of geo-localized demand.

tracking | mapping

 Tracking and mapping constitute a set of methods and processes based on digital tools and technological procedures that aims to deepen the correlation between cities/buildings socio-spatial dynamics and appropriation and its configuration and organization, combining different typological, topological and morphological approaches arranged on qualitative and quantitative standards. It explores the relationships between space users and different elements within architectural layouts and/or urban spaces (street network, building fabric, urban activities) tracking flows, collective urban dynamics and individual appropriations (using tacking devices, mobile communication devices – smartphone and tablet – and video tracking, for instance). The availability of online open source collaborative software, tracking and map apps, internet access and digital connection and platforms contributes to increase the ways to produce and to collect a wide variety of individual and collective data (big data, small data), georeferenced in real time. The goal is to track space experiences, mapping them. These topics’ arguments the convergence between tracking spaces’ dynamics and the development of social appropriation’ mapping.