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Fractal Geometry in Architecture and Design by Carl Bovill Pdf
na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.
Throughout history, nature has served as an inspiration for architecture and designers have tried to incorporate the harmonies and patterns of nature into architectural form. Alberti, Charles Renee Macintosh, Frank Lloyd Wright, and Le Courbusier are just a few of the well- known figures who have taken this approach and written on this theme. With the development of fractal geometry--the study of intricate and interesting self- similar mathematical patterns--in the last part of the twentieth century, the quest to replicate nature’s creative code took a stunning new turn. Using computers, it is now possible to model and create the organic, self-similar forms of nature in a way never previously realized. In Fractal Architecture, architect James Harris presents a definitive, lavishly illustrated guide that explains both the “how” and “why” of incorporating fractal geometry into architectural design.
The Fractal Dimension of Architecture by Michael J. Ostwald,Josephine Vaughan Pdf
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.
Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Geometric Foundations Of Design: Old And New by Jay Kappraff Pdf
This book is meant to serve either as a textbook for an interdisciplinary course in Mathematics of Design, or as a trade book for designers. It will also be of interest for people interested in recreational mathematics showing the connection between mathematics and design. Topics from the book can also be adapted for use in pre-college mathematics. Each chapter will provide the user with ideas that can be incorporated in a design. Background materials will be provided to show the reader the mathematical principles that lie behind the designs.
Architectural Geometry is the first book to introduce a revolutionary new approach to design. Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture. Written for students, architects, construction engineers, and industrial designers – Architectural Geometry is a source of inspiration for scientists interested in applications of geometry processing in architecture and art. With over 700 pages, including 2,100 full-color images of built architecture, architectural projects, and artwork, Architectural Geometry takes readers from basic to advanced geometry then leads them to the cutting-edge of research in the architectural geometry field.
Fractal Architecture by Kenneth Haggard,Polly Cooper,Christine Gyovai Pdf
Fractal Architecture: Design for Sustainability fills the gap between concepts of sustainability and the practice of environmental design. It is based on the assumption that sustainability and environmental design are not just industrial era (Modernist) design in green clothing, but a whole new direction with its own philosophy, techniques and expression. While this book is radical in the amount of change it calls for in environmental design professions and practice, it is conservative in emphasizing the traditional concerns of designers with geometry, history and aesthetics. Great effort has been made to integrate the text and graphics of this book in the spirit of holism inherent in sustainability.
Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.
Americans search for identity through a paradoxical pair of passions: spirituality and consumerism. On the one hand, we participate in religion or practice spirituality and on the other hand we are keen consumers. But, as Tom Beaudoin's Consuming Faith makes clear, if we truly seek to put our spirituality into practice, we must integrate who we are with what we buy. How are we linked to the rest of the world through our purchases? What does faith have to do with what we buy? With a new updated preface by the author, this paperback edition invites us to think about how our purchases affect who we are as individuals and as members of a global community.
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)
The Fractal Geometry of Nature by Benoit Mandelbrot Pdf
Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.
Fractals in Biology and Medicine by Gabriele A. Losa,Danilo Merlini,Theo F. Nonnenmacher,Ewald R. Weibel Pdf
In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes.
Chaos and Complexity in the Arts and Architecture by Gabriele Cappellato,Nicoletta Sala Pdf
In this compilation, the authors begin with a description of fractal geometry, its property of self-similarity, and how its processes of bifurcation can appear in the arts and architecture. These fractal features are common in different cultures and in different architectural styles. Next, the role of algebraic curves in painting, sculpture, and architecture is discussed. These shapes acted as sources of inspiration for artistic themes in many of the geometrical forms of Modern Art. Today, these beautiful shapes can be easily constructed by computers. The authors discuss an art world devoted to the entanglement phenomenon through modifying the perception of space, approaching new horizons educational fields. An investigation of the function and characteristics of fog in various paintings by famous artists of different art movements (in which the presence of fog significantly affects the visual experience) is provided. Following this, the authors describe where fractality appears in architecture and in urban organization, opening new opportunities in virtual architecture and hyperarchitecture. An additional paper presents a study on complexity in architecture. Complexity is the property of a real world system that is manifested in the inability of any one formalism being adequate to capture all of its properties. Continuing, the authors present a study shows that germs of fractals exist in old Indian literature, e.g., fractal architecture in Indian temples and fractal weapons, with the goal of collecting a few examples from old Indian history and presenting their fractal aspects. A paper is presented including some examples of industrial design objects analysed using complexity and fractal geometry. Complex and fractal components appeared in the industrial design after the development of materials, for example, the introduction of float glass. Afterwards, this book aims to show how and where the concept of time can be applied in architecture, maintaining that time is a parameter which architects seldom consider in their projects. The authors go on to illustrate some properties using Markov matrices, open symbolic dynamic nets, and fields on Julia sets, finding find both symmetrical and spiral patterns on local regions of Julia sets, and discontinuous series in the dynamics of some region that are recordable in the neurophysiology of intermittent consciousness. Synchronization can also be called self-similarity, in induced noncommutative geometry. In the next paper, new Koch curves are generated by dividing the initiator into unequal parts. With the increase in size of the set of Koch curves also comes a need for classification. Superior iterations in the study of Julia sets for rational maps are introduced, showing how new Sierpinski curve Julia sets are effectively different from those obtained by other means. Production rules to draw the new Hilbert curves are discussed, as well as production rules to draw the conventional Hilbert Curve. Later, a paper on Mandelbrot and Julia sets rendered in 3 dimensions is presented. In this paper, new Julia sets have been generated for zn+c, n 4 in superior orbit, and modelled in 3 dimensions. The authors examine the Gingko leaf, commonly referred to as a living fossil, that has been declared as tree of the millennium. This chapter aims to show that there are many ways to generate Gingko leaf. In conclusion, techniques to generate Sierpinski Gasket and Sierpinski Carpet as 3- variable and as 4-variable fractals respectively using superior iterates for contractive operators are described.
From Stockholm to Seoul, Tartu to Taipei, Spanish photographer Andres Gallardo Albajar has travelled the globe to capture the mesmerising sihouettes, colourful juxtapositions and angular forms of the world's most exciting buildings. Set against vivid skies, these buildings pop with colour, shape and geometric patterns making the book a riotous celebration of contemporary architecture.
