Mathematics in the Visual Arts

Ink and bistre wash, around 1514, Windsor, 15.7 × 20.3 cm Figure 5.5. Katabase , stone-effect polychrome plaster, 300 × 75 × 78 cm, 1991 Figure 5.6. Marches au hasard , plaster, 10,300 × 150 × 10 cm, 2012 Figure 5.7. Citadelle , plaster, 89 × 57 × 37 cm, 2010 Figure 5.8. Bifurcations (detail) – bronze, 75 × 34.5 × 30 cm, 1995 Figure 5.9. Mosaic, pool in the Place de l’Église, Fontenay-aux-Roses (destroyed...Figure 5.10. Discobolus – bronze, 70 × 50 × 50 cm, 1983–2005 Figure 5.11a. Air – bronze, 40 × 20 × 2.5 cm, 1992 Figure 5.11b. Water – bronze, 40 × 20 × 2.5 cm, 1992 Figure 5.12. Fontaine Werlé – plaster and wood, 240 × 120 × 120 cm, 1994 Figure 5.13a. Nuages – charcoal, 150 × 150 cm, 2011 Figure 5.13b. Nébuleuse – charcoal, 150 × 150 cm, 2011 Figure 5.14. Table basse – marble, 130 × 80 × 40 cm, 2001 Figure 5.15. Bistre ink, – around 1508/1509, Paris Institute, 14.6 × 10.6 cm Figure 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 Mundi 12(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 medium Figure 6.7. Vertical harmonic mesh (16 x 16) used as the compositional medium Figure 6.8. Internal geometry of the Salvator Mundi, Cook versionFigure 6.9. Internal geometry of the head of Christ Figure 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 Joseph Figure 7.3. Determining the mesh size and the composition’s original format Figure 7.4. Position of the protagonists’ heads Figure 7.5. Compositional architecture Figure 7.6. The ellipse of light Figure 7.7. The elliptical forms Figure 7.8. Internal geometry of the heads of the angel and Joseph Figure 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 Africa Figure 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...

1 Cover

2 Table of Contents

3 Title page Series Editor Marie-Christine Maurel

4 Copyright First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2020 The rights of Ruth Scheps and Marie-Christine Maurel to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2020942150 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-681-4

5 Introduction

6 Begin Reading

7 List of Authors

8 Index

9 End User License Agreement

1 v

2 iii

3 iv

4 ix

5 x

6 xi

7 xii

8 1

9 2

10 3

11 4

12 5

13 6

14 7

15 8

16 9

17 10

18 11

19 12

20 13

21 14

22 15

23 16

24 17

25 18

26 19

27 20

28 21

29 22

30 23

31 24

32 25

33 26

34 27

35 29

36 30

37 31

38 32

39 33

40 34

41 35

42 36

43 37

44 38

45 39

46 40

47 41

48 42

49 43

50 44

51 45

52 46

53 47

54 48

55 49

56 50

57 51

58 52

59 53

60 54

61 55

62 56

63 57

64 58

65 59

66 60

67 61

68 62

69 63

70 64

71 65

72 66

73 67

74 68

75 69

76 70

77 71

78 72

79 73

80 74

81 75

82 76

83 77

84 78

85 79

86 80

87 81

88 82

89 83

90 84

91 85

92 86

93 87

94 88

95 89

96 90

97 91

98 92

99 93

100 94

101 95

102 96

103 97

104 98

105 99

106 100

107 101

108 103

109 104

110 105

111 106

112 107

113 108

114 109

115 110

116 111

117 112

118 113

119 114

120 115

121 116

122 117

123 118

124 119

125 120

126 121

127 122

128 123

129 124

130 125

131 126

132 127

133 128

134 129

135 130

136 131

137 132

138 133

139 134

140 135

141 136

142 137

Читать дальше