A theoretical reflection on smart shape modeling

This paper presents, as far as the authors are aware, a complete and extended new taxonomy of shape specification modeling techniques and a characterization of shape design systems, all based on the relationship of users’ knowledge to the modeling system they use to generate shapes. In-depth knowledge of this relationship is not usually revealed in the regular university training courses such as bachelor’s, master’s and continuing education. For this reason, we believe that it is necessary to modify the learning process, offering a more global vision of all the currently existing techniques and extending training in those related to algorithmic modeling techniques. We consider the latter to be the most powerful current techniques for modeling complex shapes that cannot be modeled with the usual techniques known to date. Therefore, the most complete training should include everything from the usual geometry to textual programming. This would take us a step further along the way to more powerful design environments. The proposed taxonomy could serve as a guideline to help improve the learning process of students and designers in a complex environment with increasingly powerful requirements and tools. The term “smart” is widely used nowadays, e.g. smart phones, smart cars, smart homes, smart cities... and similar terms such as “smart shape modeling”. Nowadays, the term smart is applied from a marketing point of view, whenever an innovation is used to solve a complex problem. This is the case for what is currently called smart shape modeling. However, in the future; this concept should mean a much better design environment than today. The smart future requires better trained and skilled engineers, architects, designers or technical students. This means that they must be prepared to be able to contribute to the creation of new knowledge, to the use of innovations to solve complex problems of form, and to the extraction of the relevant pieces of intelligence from the growing volume of knowledge and technologies accessible today. Our taxonomy is presented from the point of view of methods that are possibly furthest away from what is considered today as “intelligent shape modeling” to the limit of what is achievable today and which the authors call “Generic Shape Algorithm”. Finally, we discuss the characteristics that a shape modeling system must have to be truly “intelligent”: it must be “proactive” in applying innovative ideas to achieve a solution to a complex problem

Branching Boogaloo: Botanical Adventures in Multi-Mediated Morphologies

FormaLeaf is a software interface for exploring leaf morphology using parallel string rewriting grammars called L-systems. Scanned images of dicotyledonous angiosperm leaves removed from plants around Bard’s campus are displayed on the left and analyzed using the computer vision library OpenCV. Morphometrical information and terminological labels are reported in a side-panel. “Slider mode” allows the user to control the structural template and growth parameters of the generated L-system leaf displayed on the right. “Vision mode” shows the input and generated leaves as the computer ‘sees’ them. “Search mode” attempts to automatically produce a formally defined graphical representation of the input by evaluating the visual similarity of a generated pool of candidate leaves. The system seeks to derive a possible internal structural configuration for venation based purely off a visual analysis of external shape. The iterations of the generated L-system leaves when viewed in succession appear as a hypothetical development sequence. FormaLeaf was written in Processing

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept borrowed from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical ‘coherence’ and ‘consistency’. In this study, Gabriel Pareyon presents a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. The author analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Accordingly, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature—proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. At the same time, original arguments by Benoît B. Mandelbrot (1924–2010) are revised, alongside a systematic critique of the literature on the subject. In fact, connecting Charles S. Peirce’s ‘synechism’ with Mandelbrot’s ‘fractality’ is one of the main developments of the present study

Applications of Dynamical Systems to Music Composition

Mathematics and music have long enjoyed a close working relationship: mathematicians have frequently taken an interest in the organisational principles used in music, while musicians often utilise mathematical formalisms and structures in their works. This relationship has thrived in recent years, particularly since the advent of the computer, which has allowed mathematicians and musicians alike to explore the creative aspects of various mathematical structures quickly and easily. One class of mathematical structure that is of particular interest to the technologically-minded musician is the class of dynamical systems - those that change some feature with time. This class includes fractal zooms, evolutionary computing techniques and cellular automata, each of which holds some potential as the basis of a composition algorithm. The studies that comprise this thesis were undertaken in order to further examine the relationship between mathematics and music. In particular we explore the notion that music can essentially be thought of as a type of pattern propagation: we begin with initial themes and motifs - the musical patterns - which, during the course of the composition, are subjected to certain transformations and developments according to the rules dictated by the composer or the musical form. This is exactly analogous to the process which occurs within a cellular automaton: initial configurations of cells are transformed and developed according to a set of evolution rules. We begin our study by describing the development of the CAMUS v2.0 composition software, which was based on an earlier system by Dr. Eduardo Miranda, and discuss how best to use the system to compose new musical works. The next step in our study is concerned with highlighting the limitations of CAMUS as it currently stands, and suggesting techniques for improving the capabilities of the system. We then chart the development of CAMUS 3D. At each stage we justify the changes made to the system using both aesthetic and technical arguments. We also provide a composition example, which illustrates not only the changes in operation, but also in interface. The system is then re-evaluated, and further developments are suggested

Architecture and complexity : fractal geometry as generative system

Orientador: Maria Gabriela Caffarena CelaniTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e UrbanismoResumo: Um sistema generativo (SG) de formas consiste em um método sistemático para a obtenção de soluções para um dado problema. Shape grammars, cellular automata, algoritmos genéticos e fractais são alguns exemplos de SGs que permitem a criação de composições que podem ser aplicadas em arquitetura e urbanismo. Ao longo da história os arquitetos demonstraram interesse por formas complexas e utilizaram diferentes métodos para obtê-las. Com o advento da computação alguns SGs tradicionais foram implementados em computador ampliando as possibilidades de obtenção de formas complexas. Paralelamente, o surgimento dos meios de produção pós-industriais no final do século XX tornou possível a produção dessas formas com relativa facilidade e economia. Além disso, a renovação do ornamento na arquitetura contemporânea tem despertado o interesse para composições complexas. Dentre os SGs que têm sido utilizados por arquitetos contemporâneos, os fractais são particularmente interessantes porque permitem a geração de formas complexas a partir de regras simples em um processo inteligível no qual o controle por parte do projetista é mantido. Contudo, para que um arquiteto se aproprie efetivamente deste método, se faz necessária a introdução de uma série de conhecimentos e habilidades, bem como de um arcabouço teórico. Esta tese investiga o projeto de arquitetura utilizando geometria fractal (GF) e propõe maneiras de abordar esses conteúdos com o apoio de teorias e ferramentas contemporâneas, como os SGs de projeto, a modelagem paramétrica, os ambientes de programação de CAD e a fabricação digital. A metodologia desta pesquisa exploratória incluiu a revisão bibliográfica, análise de exemplos, entrevistas com arquitetos e experimentações com a GF como SG. Foi possível averiguar que a GF pode ser um método eficaz e factível, tendo em vista a disponibilidade de equipamentos de fabricação digital, para a geração de complexidade na arquiteturaAbstract: A generative system of shapes is a systematic method to achieve solutions for a design problem. Shape grammars, cellular automata, genetic algorithms and fractals are some examples of generative systems that enable the creation of compositions to be applied in architecture and urban design. Throughout history the architects were interested by complex shapes and have used different methods to obtain complexity. With the use of computation some classic generative systems were implemented on computers expanding the possibilities to obtain complex shapes. At the same time, the arising of post-industrial means of production in the end of XX century made possible the production of those shapes easily and with economic viability. Moreover, the renovation of the ornament concept in the contemporary architecture is directly related to complex compositions. Among the generative systems that have been used by contemporary architects, fractals are particularly interesting because they generate complex shapes from simple rules in an intelligible process in which the designer control is preserved. However, to architects use fractals consistently, they must understand some concepts and acquire some abilities, and the architect must comprehend a theoretical framework. This thesis is an investigation of the design process that uses fractal geometry and it proposes ways of approach this subject with the support of theory and contemporary tools, as computational design and digital fabrication. The methodology of this exploratory research includes the literature review, case studies, interviews and applicatios of fractal geometry as generative system. It was possible to ascertain that the fractals may be an effective and feasible method, considering the digital fabrication equipments available, for the generation of complexity in architectureDoutoradoArquitetura, Tecnologia e CidadeDoutor em Arquitetura, Tecnologia e Cidade2014/13572-50203267/2014-1FAPESCNPQCAPE

Matrix Graph Grammars

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.Comment: 321 pages, 75 figures. This book has is publisehd by VDM verlag, ISBN 978-363921255

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers