The Structure of Paintings (eBook)

Michael Leyton's mathematical work on shape has been used by scientists in over 40 disciplines from chemical engineering to meteorology. His scientific contributions have received major prizes, such as a presidential award and a medal for scientific achievement. His new foundations to geometry are elaborated in his books in Springer-Verlag and MIT Press. Besides his scientific and mathematical work, he is also a highly exhibited painter and sculptor, and his architecture designs have been published by Birkhauser-Architectural. Also he is the composer of published string quartets. He is president of the International Society for Mathematical and Computational Aesthetics, and is on the faculty of the Psychology Department and the DIMACS Center for Discrete Mathematics and Theoretical Computer Science at Rutgers.

Contents 5
Shape as Memory Storage 7
1.1 Introduction 7
1.2 New Foundations to Geometry 8
1.3 TheWorld as Memory Storage 11
1.4 The Fundamental Laws 12
1.5 The Meaning of an Artwork 16
1.6 Tension 17
1.7 Tension in Curvature 18
1.8 Curvature Extrema 19
1.9 Symmetry in Complex Shape 20
1.10 Symmetry-Curvature Duality 23
1.11 Curvature Extrema and the Symmetry Principle 24
1.12 Curvature Extrema and the Asymmetry Principle 25
1.13 General Shapes 27
1.14 The Three Rules 27
1.15 Process Diagrams 29
1.16 Trying out the Rules 29
1.17 How the Rules Conform to the Procedure for Re-covering the Past 30
1.18 Applying the Rules to Artworks 33
1.19 Case Studies 33
1.20 The Fundamental Laws of Art 47
Expressiveness of Line 49
2.1 Theory of Emotional Expression 49
2.2 Expressiveness of Line 51
2.3 The Four Types of Curvature Extrema 51
2.4 Process-Arrows for the Four Extrema 53
2.5 Historical Characteristics of Extrema 54
2.6 The Role of the Historical Characteristics 69
2.7 The Duality Operator 71
2.8 Picasso: 74
The Evolution Laws 79
3.1 Introduction 79
3.2 Process Continuations 81
3.3 Continuation at 81
and 81
3.4 Continuation at 82
3.5 Continuation at 85
3.6 Bifurcations 89
3.7 Bifurcation at 89
3.8 Bifurcation at 92
3.9 The Bifurcation Format 95
3.10 Bifurcation at 95
3.11 Bifurcation at 98
3.12 The Process-Grammar 101
3.13 The Duality Operator and the Process-Grammar 103
3.14 Holbein: 105
3.15 The Entire History 120
3.16 History on the Full Closed Shape 122
3.17 Gauguin: 128
3.18 Memling: 130
3.19 Tension and Expression 133
Smoothness-Breaking 135
4.1 Introduction 135
4.2 The Smoothness-Breaking Operation 137
4.3 Cusp-Formation 140
4.4 Always the Asymmetry Principle 142
4.5 Cusp-Formation in Compressive Extrema 143
4.6 The Bent Cusp 146
4.7 Picasso: 148
4.8 The Meaning of 157
4.9 Balthus: 159
4.10 Balthus: 173
4.11 Ingres: 182
4.12 Modigliani: 195
4.13 The Complete Set of Extrema-Based Rules 202
4.14 Final Comments 204
Bibliography 207
Credits 209
Index 211
Color Plates 214