Mathematics in the Visual Arts. Группа авторов

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      List of Illustrations

      1 Chapter 1Figure 1.1. Giotto di Bondone, Life of St. Francis, fresco, around 1290. Assisi,...Figure 1.2. Ambrogio Lorenzetti, Annunciation, tempera on wood, Siena, Pinacotec...Figure 1.3. Antonello da Messina, St. Sebastian, tempera on wood transposed onto...Figure 1.4. Brunelleschi’s experiment with linear perspective, looking through t...Figure 1.5. Andrea Mantegna, Study for the Dead Christ, pen and brown wash on pa...Figure 1.6. Paolo Uccello, Battle of San Romano, detail, 1456, tempera on wood. ...Figure 1.7. Andrea Mantegna, The Dead Christ, tempera on canvas, Milan, Pinacote...Figure 1.8. Piero della Francesca, Polyptych of Perugia, 1470, Perugia, National...Figure 1.9. Polyptych of Perugia, upper register (see Figure 1.8)Figure 1.10. De Martone, art. cit.Figure 1.11. Paolo Uccello, Battle of San Romano, 1456, tempera on wood. London,...

      2 Chapter 2Figure 2.1. Reuven Berman Kadim, Hovering Object #1. Digital image, 199711Figure 2.2. Reuven Berman Kadim, Paving B, Digital Image, 199612Figure 2.3. Emmanuel Van der Meulen, Quadrum, 2017, acrylic on canvas, 130 × 130...Figure 2.4. Emmanuel Van der Meulen, Bethel, 2017, acrylic on canvas, 130 × 130 ...Figure 2.5. Esther Stocker, Untitled, 2010, acrylic on canvas, 200 × 300 cm. Cou...Figure 2.6. Esther Stocker, Unlimited Space, 2013, Roudnice, Czech Republic. Cou...

      3 Chapter 3Figure 3.1. Examples of Luca Caciagli’s Komorebi project, showing fractals in na...Figure 3.2. Examples of simple mathematical fractals, from left to right: the Ko...Figure 3.3. Examples of Luca Caciagli’s Komorebi project, showing contradictions...Figure 3.4. René Magritte, Le blanc-seing (The Blank Signature in English), oil ...Figure 3.5. Simon Hantaï, Étude, oil on canvas, 275 × 238 cm, 1969. National Gal...Figure 3.6. An example of where fractals can be found in the stock market

      4 Chapter 4Figure 4.1. Drawing by Leonardo da Vinci. Courtesy of the Library of the Institu...Figure 4.2. Remanta microdrone. Courtesy of ONERAFigure 4.3. Drawing by Leonardo da Vinci of bat wings and Clément Ader's Eole in...Figure 4.4. Marey’s Smoke wind tunnelFigure 4.5. Visualizations created by Marey. Courtesy of Cinémathèque françaiseFigure 4.6. ONERA’s water tunnel at Châtillon (Hauts-de-Seine)Figure 4.7. Visualizations of vortex windings on Concorde. Courtesy of ONERAFigure 4.8. Visualization from the water tunnel of a Citroën DS. Courtesy of ONE...Figure 4.9. The Mirror 1994. Marble, 100 × 49 × 49 cm visualization of an ellips...Figure 4.10. Interférences de chocs, 2005, Stuc, 61 × 7 cm, International Year o...Figure 4.11. Schlieren visualizations carried out at ONERA’s R3Ch wind tunnel in...

      5 Chapter 5Figure 5.1. Ink, around 1510/1513, Windsor, 15 × 17 cmFigure 5.2. Leda, black stone and ink, around 1505/1510, Windsor, 20 × 16.2 cmFigure 5.3. Ink, around 1515, Venice, Accademia Gallery, 9.6 × 14.9 cmFigure 5.4. Ink and bistre wash, around 1514, Windsor, 15.7 × 20.3 cmFigure 5.5. Katabase, stone-effect polychrome plaster, 300 × 75 × 78 cm, 1991Figure 5.6. Marches au hasard, plaster, 10,300 × 150 × 10 cm, 2012Figure 5.7. Citadelle, plaster, 89 × 57 × 37 cm, 2010Figure 5.8. Bifurcations (detail) – bronze, 75 × 34.5 × 30 cm, 1995Figure 5.9. Mosaic, pool in the Place de l’Église, Fontenay-aux-Roses (destroyed...Figure 5.10. Discobolus – bronze, 70 × 50 × 50 cm, 1983–2005Figure 5.11a. Air – bronze, 40 × 20 × 2.5 cm, 1992Figure 5.11b. Water – bronze, 40 × 20 × 2.5 cm, 1992Figure 5.12. Fontaine Werlé – plaster and wood, 240 × 120 × 120 cm, 1994Figure 5.13a. Nuages – charcoal, 150 × 150 cm, 2011Figure 5.13b. Nébuleuse – charcoal, 150 × 150 cm, 2011Figure 5.14. Table basse – marble, 130 × 80 × 40 cm, 2001Figure 5.15. Bistre ink, – around 1508/1509, Paris Institute, 14.6 × 10.6 cmFigure 5.16. Saint-Exupéry Medal – recto/verso, diameter 8.4 cm – Monnaie de Par...Figure 5.17. The Saint-Exupéry Stele – bronze, 202 × 75 × 75 cm, 2000

      6 Chapter 6Figure 6.1. Leonardo da Vinci: Salvator Mundi12 (so-called Cook version) (Louvre...Figure 6.2. Study for the Salvator MundiFigure 6.3. The outline of the skull has the form of an elliptical arc (Royal Co...Figure 6.4. The semi-axes (a and b) of the ellipse form a harmonic rectangleFigure 6.5. The subdivision (3 x 3) of this rectangle determines a vertical harm...Figure 6.6. Vertical harmonic mesh (16 x 16) used as the compositional mediumFigure 6.7. Vertical harmonic mesh (16 x 16) used as the compositional mediumFigure 6.8. Internal geometry of the Salvator Mundi, Cook versionFigure 6.9. Internal geometry of the head of ChristFigure 6.10. Internal geometry of the head of the Mona LisaFigure 6.11. Properties of the type 1 ellipse modeling the head of the Salvator....Figure 6.12. Lady with an Ermine (detail) a band of interlacing runs down the ri...Figure 6.13. Study of interlacing (Leonardo da Vinci)Figure 6.14. The stole’s two bands and the patterns formed by the filigree, mode...Figure 6.15. Representation of the path taken by the filigree on the stole’s int...Figure 6.16. The various modules of the filigree’s journey. The first three are ...Figure 6.17. The internal geometry of the Salvator Mundi, Cook Version and of th...Figure 6.18. Details of the interlacing on the intersecting bands on the Salvato...

      7 Chapter 7Figure 7.1. Georges de La Tour: The Apparition of the Angel to St. Joseph, oil o...Figure 7.2. Modeling the heads of the angel and JosephFigure 7.3. Determining the mesh size and the composition’s original formatFigure 7.4. Position of the protagonists’ headsFigure 7.5. Compositional architectureFigure 7.6. The ellipse of lightFigure 7.7. The elliptical formsFigure 7.8. Internal geometry of the heads of the angel and JosephFigure 7.9. Compositional construction

      8 Chapter 8Figure 8.1. Tableau scénique no. 1 by Sophie Lavaud – modeling of elements of th...Figure 8.2. Tableau scénique 2.0 by Sophie Lavaud – modeling of elements of the ...Figure 8.3. Tableau scénique 2.0 by Sophie Lavaud – a viewer interacting with th...Figure 8.4. GAMA software (version 1.6.1) interface – simulation view – screensh...Figure 8.5. Agents initially placed randomly (t = 0) create a circular form over...Figure 8.6. Emergence of a spiral within a group of 64 agents. Three snapshots t...Figure 8.7. Emergence of the flashing effect in three states. Snapshots of the t...Figure 8.8a. Aerial view of tiger bush in AfricaFigure 8.8b. Emergence of irregular bands, in a group of 2,500 oriented agents, ...Figure 8.9. Representation of the predator–prey model in GAMA. Left: the initial...Figure 8.10a. Representation of the predator–prey model in GAMA. Emergence of pa...Figure 8.10b. Same representation of the predator–prey model as in Figure 8.10a,...Figure 8.11. Representation of the predator–prey model in a color space with a g...Figure 8.12. Illustration of the predator–prey model in a colors space with a gr...Figure 8.13. Representation of the predator–prey model with five agents in secti...Figure 8.14. Representation of the predator–prey model with five agents by overl...

      Guide

      1  Cover

      2 Table of Contents

      3  Title page

      4  Copyright

      5  Introduction

      6  Begin Reading

      7 

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