Adamatzky, A. (2010) Physarum machines: computers from slime mould. (74) World Scientific Publishing. ISBN 978-981-4327-58-9 We recommend you cite the published version. The publisher s URL is Refereed: No Physarum Machines: computers from slime mould, Andrew Adamatzky, Copyright? 2010 World Scientific Publishing Co. with permission from World Scientific Publishing Co. Pte. Ltd. Disclaimer UWE has obtained warranties from all depositors as to their title in the material deposited and as to their right to deposit such material. UWE makes no representation or warranties of commercial utility, title, or fitness for a particular purpose or any other warranty, express or implied in respect of any material deposited. UWE makes no representation that the use of the materials will not infringe any patent, copyright, trademark or other property or proprietary rights. UWE accepts no liability for any infringement of intellectual property rights in any material deposited but will remove such material from public view pending investigation in the event of an allegation of any such infringement. PLEASE SCROLL DOWN FOR TEXT.
Contents Preface Acknowledgments v ix 1. From reaction diffusion to Physarum computing 1 1.1 Reaction diffusion computers............... 2 1.2 Limitations of reaction diffusion computers....... 4 1.3 Physarum polycephalum.................. 5 1.4 Physarum as encapsulated reaction diffusion computer 8 1.5 Dawn of Physarum computing.............. 12 2. Experimenting with Physarum 15 2.1 Where to get plasmodium of P. polycephalum...... 15 2.2 Physarum farms...................... 15 2.3 Dishes and scanners.................... 18 2.4 Data input with food................... 19 2.5 Substrates......................... 20 2.6 Nutrient-rich vs. non-nutrient substrates........ 24 2.7 Sensing........................... 28 2.8 Modeling plasmodium................... 34 2.9 Summary.......................... 35 3. Physarum solves mazes 37 3.1 Multiple-site start..................... 37 3.2 Single-site start...................... 38 3.3 Summary.......................... 42 xi
xii Physarum machines 4. Plane tessellation 43 4.1 The ubiquitous diagram.................. 43 4.2 Physarum construction of Voronoi diagram....... 44 4.3 Summary.......................... 47 5. Oregonator model of Physarum growing trees 53 5.1 What a BZ medium could not do............ 55 5.2 Physarum and Oregonator................ 55 5.3 Building trees with Oregonator.............. 58 5.4 Validating simulation by experiments.......... 60 5.5 Summary.......................... 60 6. Does the plasmodium follow Toussaint hierarchy? 65 6.1 Proximity graphs...................... 65 6.1.1 Nearest-neighborhood graph........... 67 6.1.2 Minimal spanning tree.............. 67 6.1.3 Relative neighborhood graph.......... 67 6.1.4 Gabriel graph................... 67 6.1.5 Delaunay triangulation.............. 67 6.1.6 Toussaint hierarchy................ 68 6.2 Plasmodium network and Toussaint hierarchy..... 68 6.3 Preparing for graph growing............... 70 6.4 Growing graph from a single point............ 72 6.5 Growing from all points.................. 80 6.6 Physarum hierarchy.................... 85 6.7 Summary.......................... 85 6.7.1 Complexity of plasmodium computation.... 86 6.7.2 Halting problem.................. 86 6.7.3 Reusability.................... 86 6.7.4 Further studies.................. 87 7. Physarum gates 89 7.1 xor gate anyone?..................... 90 7.2 Ballistics of Physarum localizations........... 93 7.3 Physarum gates...................... 95 7.4 Simulation of Physarum gates.............. 101 7.5 Simulated one-bit half-adder............... 105 7.6 Why do we use a non-nutrient substrate?........ 107
Contents xiii 7.7 Summary.......................... 107 8. Kolmogorov Uspensky machine in plasmodium 109 8.1 Physarum machines.................... 111 8.1.1 Materials for Physarum machine........ 111 8.1.2 Nodes....................... 112 8.1.3 Edges....................... 113 8.1.4 Data, results and halting............. 114 8.1.5 Active zone.................... 115 8.1.6 Bounded connectivity............... 115 8.1.7 Addressing and labeling............. 116 8.1.8 Basic operations.................. 118 8.2 Example of Physarum machine solving simple task... 120 8.3 On parallelism....................... 122 8.4 Summary.......................... 123 9. Reconfiguring Physarum machines with attractants 125 9.1 Fusion and multiplication of active zones........ 125 9.2 Translating active zone.................. 129 9.3 Reconfiguration of Physarum machine.......... 130 9.4 Summary.......................... 132 10. Programming Physarum machines with light 135 10.1 Physarum and light.................... 135 10.2 Designing control domains................ 137 10.3 Trees and waves...................... 138 10.4 Diverting plasmodium................... 141 10.5 Inertia............................ 141 10.6 Multiplying plasmodium waves.............. 146 10.7 Foraging around obstacles................. 147 10.8 Routing signals in Physarum machine.......... 151 10.9 Disobedience........................ 154 10.10 Summary.......................... 156 11. Routing Physarum with repellents 159 11.1 Avoiding repellents on nutrient-rich substrate...... 161 11.2 Operating on non-nutrient substrate........... 162 11.3 Operation deflect.................... 164
xiv Physarum machines 11.4 Operation multiply.................... 164 11.5 Operation merge..................... 167 11.6 Summary.......................... 170 12. Physarum manipulators 175 12.1 Plasmodium on water surface............... 176 12.2 Manipulating floating objects............... 179 12.3 Summary.......................... 184 13. Physarum boats 185 13.1 Random wandering.................... 187 13.2 Sliding........................... 188 13.3 Pushing........................... 188 13.4 Anchoring.......................... 189 13.5 Propelling.......................... 190 13.6 Cellular automaton model................. 192 13.7 Physarum tugboat..................... 196 13.8 On failures......................... 196 13.9 Summary.......................... 199 14. Manipulating substances with Physarum machine 201 14.1 Operations with colored substances........... 201 14.2 Transfer of substances to specified location....... 207 14.3 Mixing substances..................... 209 14.4 Superpositions of transfer and mix operations.... 213 14.5 Summary.......................... 215 15. Road planning with slime mould 223 15.1 United Kingdom in a gel................. 225 15.2 Development of transport links.............. 228 15.3 Weighted Physarum graphs................ 231 15.4 Physarum vs. Department for Transport........ 234 15.5 Proximity graphs and motorways............. 236 15.6 Imitating disasters..................... 238 15.7 Summary.......................... 243 Epilogue 247 Bibliography 249 Index 261