Chaos and Complexity in the Arts and Architecture: Research in Progress

Nicoletta Sala (Editor)
Institute for Complexity Study, Rome, Italy
CERFIM (Research Center for Mathematics and Physics), Locarno, Switzerland
ISSI (Institute for Scientific and Interdisciplinary Studies), Locarno, Switzerland

Gabriele Cappellato (Editor)
Accademia di Architettura di Mendrisio, University of Lugano, Switzerland

Series: Mathematics Research Developments
BISAC: ARC009000

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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. (Imprint: Nova)

Preface

Chapter 1. Fractality in the Arts and in Architecture
(Gabriele Cappellato and Nicoletta Sala, Accademia di Architettura di Mendrisio, University of Lugano, Switzerland, Institute for Complexity Study, Rome, Italy, and others)

Chapter 2. Algebraic Curves and Varieties in XX Century Art
(Vincenzo Iorfida, PhD, Mauro Francaviglia, and Marcella Giulia Lorenzi, School "Archimedes", University of Calabria, Campus of Arcavacata, Rende CS, Italy, and others)

Chapter 3. From Quantum Models to Mathematical and Conceptual Structure of the XXth Century Art
(Vincenzo Iorfida, University of Calabria, Campus of Arcavacata, Via P. Bucci, Rende CS, Italy)

Chapter 4. Investigating Complexity in Foggy Paintings by CNN-Based Techniques
(Arturo Buscarino, Luigi Fortuna, Mattia Frasca, Angelo Lamia, and Maria Gabriella Xibilia, University of Catania, DIEEI, Catania, Italy)

Chapter 5. Fractals in Architecture: Hyperarchitecture and Beyond
(Nicoletta Sala, Accademia di Architettura di Mendrisio, Università della Svizzera Italiana, Svizzera)

Chapter 6. Complexity and Architecture
(Nicoletta Sala, Accademia di Architettura, Università della Svizzera italiana, Mendrisio, Switzerland)

Chapter 7. Vedic Fractals
(Mamta Rani, Sanjaya Tripathi, and Arun Prakash Agarwal, Krishna Engineering College, Ghaziabad, India)

Chapter 8. Fractal Geometry in Virtual Worlds and in Second Life
(Nicoletta Sala, Accademia di Architettura, Università della Svizzera italiana, Largo Bernasconi, Mendrisio, Switzerland, and others)

Chapter 9. Complexity and Fractality in Industrial Design
(Nicoletta Sala, Accademia di Architettura Università della Svizzera italiana, Mendrisio, Switzerland)

Chapter 10. Architecture and Time
(Nicoletta Sala, Accademia di Architettura, Università della Svizzera italiana, University of Lugano, Mendrisio, Switzerland)

Chapter 11. Synchronization of Fractals in Logarithmic Spirals
(Robert A. M. Gregson, Australian National University, Canberra, ACT, Australia)

Chapter 12. New Koch Curves and Their Classification
(Mamta Rani, Riaz Ul Haq, and Norrozila Sulaiman, Krishna Engineering College, Ghaziabad, India)

Chapter 13. New Sierpinski Curve Julia Sets
(Manish Kumar and Mamta Rani, DNM Institute of Engineering & Technology, Lucknow, India)

Chapter 14. New Hilbert Curves
(Saurabh Goel and Mamta Rani, Department of Computer Science, KCC Institute of Technology and Management, Greater Noida, India)

Chapter 15. 3D Superior Julia Sets for nth Degree Polynomial zn + c, n 4
(Mamta Rani, Deepak K. Verma and J. S. Sodhi, Department of Computer Applications, Krishna Engineering College, Ghaziabad, India)

Chapter 16. Gingko Leaves
(Mamta Rani and Bharti Singh, Central University of Rajasthan, Kishangarh, Rajasthan, India)

Chapter 17. V-Variable Sierpinski Gasket and Carpet
(Mamta Rani, R. C. Dimri, and Darshana J. Prajapati, Faculty of Computer Systems and Software Engg., University Malaysia Pahang, Lebuhraya Tun Razak, Gambang, Kuantan, Malaysia)

Index

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