Reaction-diffusion computers

The book introduces a hot topic of novel and emerging computing paradigms and architectures -computation by travelling waves in reaction-diffusion media. A reaction-diffusion computer is a massively parallel computing device, where the micro-volumes of the chemical medium act as elementary few-bit processors, and chemical species diffuse and react in parallel. In the reaction-diffusion computer both the data and the results of the computation are encoded as concentration profiles of the reagents, or local disturbances of concentrations, whilst the computation per se is performed via the spreading and interaction of waves caused by the local disturbances. The monograph brings together results of a decade-long study into designing experimental and simulated prototypes of reaction-diffusion computing devices for image processing, path planning, robot navigation, computational geometry, logics and artificial intelligence. The book is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, and cutting-edge computation techniques, chemical laboratory experimental setups and hardware implementation technology employed in the development of novel nature-inspired computing devices.

Key Features:

- Non-classical and fresh approach to theory of computation. - In depth exploration of novel and emerging paradigms of nature-inspired computing. - Simple to understand cellular-automata models will help readers/students to design their own computational experiments to advance ideas and concepts described in the book . - Detailed description of receipts and experimental setups of chemical laboratory reaction-diffusion processors will make the book an invaluable resource in practical studies of non-classical and nature-inspired computing architectures . - Step by step explanations of VLSI reaction-diffusion circuits will help students to design their own types of wave-based processors.

Author Notes

Andy Adamatzky is Professor at the Faculty of Computing, Engineering and Mathematical Sciences, University of the West of England, Bristol, UK
Ben de Lacy Costello is Senior Research Fellow at the Centre for Research in Analytical, Material and Sensor Sciences, Faculty of Applied Science, University of the West of England, Bristol, UK
Tetsuya Asai is Associate Professor at the Graduate School of Information Science and Technology, Hokkaido University, Japan

Preface	p. v
Contents	p. xiii
1 Non-linear chemistry meets non-classical computation	p. 1
1.1 What is a chemical processor?	p. 2
1.2 Overview of chemical processors	p. 7
1.3 Other chemical systems	p. 22
1.4 Current state of reaction-diffusion processors	p. 25
2 Geometrical computation: Voronoi diagram and skeleton	p. 31
2.1 Voronoi diagram	p. 31
2.2 Time-to-space mapping	p. 33
2.3 Cellular-automaton Voronoi diagram	p. 34
2.4 Chemical processors for Voronoi-diagram computation	p. 41
2.5 Voronoi diagrams in chemical processors	p. 43
2.6 When computations go wrong!	p. 50
2.7 Unstable processors	p. 52
2.8 Secondary Voronoi diagrams	p. 57
2.9 Controllability of secondary Voronoi diagrams	p. 61
2.10 Skeleton of planar shape	p. 64
2.11 Chemical processors for skeleton computation	p. 65
2.12 Mechanics of skeletonisation	p. 65
2.13 Computing skeletons of geometric shapes	p. 70
2.14 Multitasking in chemical processors	p. 72
2.15 Conclusion	p. 79
3 Logical circuits in chemical media	p. 83
3.1 Logical gates in precipitating medium	p. 84
3.2 Collision-based computing in excitable media	p. 92
3.3 Laboratory prototype of collision-based computer	p. 97
3.4 Hexagonal reaction-diffusion automaton	p. 107
3.5 Conclusion	p. 114
4 Reaction-diffusion controllers for robots	p. 119
4.1 Robot taxis controlled by a Belousov-Zhabotinsky medium	p. 119
4.2 Path planning	p. 128
4.3 Controlling a robotic hand	p. 148
4.4 Conclusion	p. 156
5 Programming reaction-diffusion processors	p. 161
5.1 Controllability	p. 161
5.2 How to program reaction-diffusion computers?	p. 162
5.3 Programming with reaction rates	p. 164
5.4 Programming with excitability	p. 167
5.5 Conclusion	p. 176
6 Silicon reaction-diffusion processors	p. 177
6.1 Modelling reaction-diffusion LSI circuits	p. 179
6.2 Digital reaction-diffusion chips	p. 183
6.3 Analogue reaction-diffusion chips	p. 210
7 Minority-carrier reaction-diffusion device	p. 247
7.1 Reaction-diffusion computing device with p-n-p-n diode	p. 247
7.2 Numerical simulation results	p. 256
7.3 Computing in reaction-diffusion semiconductor devices	p. 260
7.4 Conclusion	p. 262
8 Single-electron reaction-diffusion devices	p. 263
8.1 Constructing electrical analogue of reaction-diffusion systems	p. 263
8.2 Spatio-temporal dynamics produced by the single-electron system	p. 269
8.3 Towards actual reaction-diffusion devices	p. 272
9 Non-constructibility: from devil's advocate	p. 275
9.1 Computing with singularities	p. 275
9.2 Voronoi diagram is not invertible	p. 283
9.3 Conclusion	p. 288
Glossary	p. 289
Colour insert	p. 297
Bibliography	p. 309
Index	p. 331

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Table of Contents