vi
2. Combinatorics of shortest paths 33
3. Combinations of paths 43
4. Outlook 49
5. Further reading 50
6. Solutions to the questions 51
Chapter 5. Romeo and Juliet, Spontaneous Pattern Formation, and Turing’s
Instability
Bernold Fiedler 53
1. Turing dreams 53
2. Romeo and Juliet 54
3. Roberto and Julietta 55
4. When sisters gossip . . . 57
5. . . . and brothers brag 60
6. Turing’s theorem 63
7. Mathematical summary 64
8. Outlook 66
References 69
Chapter 6. Mathematics and Intelligent Materials
Stefan Muller
¨
71
Mathematics as a key technology 71
Metals with memory 71
Memory and microstructure 71
Microstructures everywhere 74
Microstructures as optimal forms 75
Mathematical chance helps—Young measures 76
Design of new materials through mathematics 77
Future challenges: multiscale mathematics,
or the bridging from atoms to materials 77
Protein folding, rough energy landscapes, and optimization 80
References 80
Chapter 7. Discrete Tomography: From Battleship to Nanotechnology
Peter Gritzmann 81
A glimpse into the human body 81
Behind the teacher’s back 82
Duty rosters and data security 87
Reconstruction of crystalline structures 87
Uniqueness theorems 91
Complexity and algorithms 95
Stability 96
Chapter 8. Reflections on Reflections
Jurgen
¨
Richter-Gebert 99
Childhood memories 99
1. Good angles, bad angles 99
2. One, two, three . . . infinity 101
3. Kaleidoscopes—beauty-viewers 101
4. Number games 103
CONTENTS
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