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Computers from Plants We Never Made: Speculations

  • Andrew AdamatzkyEmail author
  • Simon Harding
  • Victor Erokhin
  • Richard Mayne
  • Nina Gizzie
  • Frantisek Baluška
  • Stefano Mancuso
  • Georgios Ch. Sirakoulis
Part of the Emergence, Complexity and Computation book series (ECC, volume 28)

Abstract

Plants are highly intelligent organisms. They continuously make distributed processing of sensory information, concurrent decision making and parallel actuation. The plants are efficient green computers per se. Outside in nature, the plants are programmed and hardwired to perform a narrow range of tasks aimed to maximize the plants’ ecological distribution, survival and reproduction. To ‘persuade’ plants to solve tasks outside their usual range of activities, we must either choose problem domains which homomorphic to the plants natural domains or modify biophysical properties of plants to make them organic electronic devices. We discuss possible designs and prototypes of computing systems that could be based on morphological development of roots, interaction of roots, and analog electrical computation with plants, and plant-derived electronic components. In morphological plant processors data are represented by initial configuration of roots and configurations of sources of attractants and repellents; results of computation are represented by topology of the roots’ network. Computation is implemented by the roots following gradients of attractants and repellents, as well as interacting with each other. Problems solvable by plant roots, in principle, include shortest-path, minimum spanning tree, Voronoi diagram, \(\alpha \)-shapes, convex subdivision of concave polygons. Electrical properties of plants can be modified by loading the plants with functional nanoparticles or coating parts of plants of conductive polymers. Thus, we are in position to make living variable resistors, capacitors, operational amplifiers, multipliers, potentiometers and fixed-function generators. The electrically modified plants can implement summation, integration with respect to time, inversion, multiplication, exponentiation, logarithm, division. Mathematical and engineering problems to be solved can be represented in plant root networks of resistive or reaction elements. Developments in plant-based computing architectures will trigger emergence of a unique community of biologists, electronic engineering and computer scientists working together to produce living electronic devices which future green computers will be made of.

References

  1. 1.
    Adamatzky, A.: Collision-Based Computing. Springer (2002)Google Scholar
  2. 2.
    Adamatzky, A.: Hot ice computer. Phys. Lett. A 374(2), 264–271 (2009)CrossRefGoogle Scholar
  3. 3.
    Adamatzky, A.: Physarum Machines: Computers from Slime Mould. World Scientific (2010)Google Scholar
  4. 4.
    Adamatzky, A.: Slime mould computes planar shapes. Int. J. Bio-Inspir. Comput. 4(3), 149–154 (2012)CrossRefGoogle Scholar
  5. 5.
    Adamatzky, A.: Towards plant wires. Biosystems 122, 1–6 (2014)CrossRefGoogle Scholar
  6. 6.
    Adamatzky, A. (ed.): Advances in Physarum Machines: Sensing and Computing with Slime Mould. Springer (2016)Google Scholar
  7. 7.
    Adamatzky, A., Armstrong, R., De Lacy Costello, B., Deng, Y., Jones, J., Mayne, R., Schubert, T., Sirakoulis, G.Ch., Zhang, X.: Slime mould analogue models of space exploration and planet colonisation. J. Br. Interplanet. Soc. 67, 290–304 (2014)Google Scholar
  8. 8.
    Adamatzky, A., Costello, B.D.L., Asai, T.: Reaction-Diffusion Computers. Elsevier (2005)Google Scholar
  9. 9.
    Adamatzky, A., Holley, J., Bull, L., Costello, B.D.L.: On computing in fine-grained compartmentalised Belousov-Zhabotinsky medium. Chaos Solitons Fractals 44(10), 779–790 (2011)Google Scholar
  10. 10.
    Adamatzky, A., Kitson, S., Costello, B.D.L., Matranga, M.A., Younger, D.: Computing with liquid crystal fingers: Models of geometric and logical computation. Phys. Rev. E 84(6), 061,702 (2011)Google Scholar
  11. 11.
    Adamatzky, A., Sirakoulis, G.Ch., Martinez, G.J., Baluska, F., Mancuso, S.: On plant roots logical gates. arXiv preprint arXiv:1610.04602 (2016)
  12. 12.
    Adleman, L.M., McCurley, K.S.: Open problems in number theoretic complexity, ii. In: International Algorithmic Number Theory Symposium, pp. 291–322. Springer (1994)Google Scholar
  13. 13.
    Akl, S.G.: Parallel Sorting Algorithms, vol. 12. Academic press (2014)Google Scholar
  14. 14.
    Bais, H.P., Park, S.W., Weir, T.L., Callaway, R.M., Vivanco, J.M.: How plants communicate using the underground information superhighway. Trends Plant Sci. 9(1), 26–32 (2004)CrossRefGoogle Scholar
  15. 15.
    Bais, H.P., Weir, T.L., Perry, L.G., Gilroy, S., Vivanco, J.M.: The role of root exudates in rhizosphere interactions with plants and other organisms. Annu. Rev. Plant Biol. 57, 233–266 (2006)CrossRefGoogle Scholar
  16. 16.
    Baluška, F., Mancuso, S.: Plant neurobiology as a paradigm shift not only in the plant sciences. Plant Signal. Behav. 2(4), 205–207 (2007)CrossRefGoogle Scholar
  17. 17.
    Baluška, F., Mancuso, S.: Deep evolutionary origins of neurobiology: turning the essence of’neural’upside-down. Commun. Integr. Biol. 2(1), 60–65 (2009)CrossRefGoogle Scholar
  18. 18.
    Baluška, F., Mancuso, S.: Plant neurobiology: from sensory biology, via plant communication, to social plant behavior. Cognit. Process. 10(1), 3–7 (2009)CrossRefGoogle Scholar
  19. 19.
    Baluška, F., Mancuso, S.: Vision in plants via plant-specific ocelli? Trends Plant Sci. 21(9), 727–730 (2016)CrossRefGoogle Scholar
  20. 20.
    Baluška, F., Mancuso, S., Volkmann, D. (eds.): Communication in Plants: Neuronal Aspects of Plant Life. Springer (2007)Google Scholar
  21. 21.
    Baluška, F., Mancuso, S., Volkmann, D.: Communication in plants. In: Neuronal Aspect of Plant Life. Spriger, Heidelberg (2006)Google Scholar
  22. 22.
    Baluška, F., Mancuso, S., Volkmann, D., Barlow, P.: Root apices as plant command centres: the unique brain-like status of the root apex transition zone. Biologia (Bratisl.) 59(Suppl. 13), 1–13 (2004)Google Scholar
  23. 23.
    Baluška, F., Mancuso, S., Volkmann, D., Barlow, P.W.: Root apex transition zone: a signalling-response nexus in the root. Trends Plant Sci. 15(7), 402–408 (2010)CrossRefGoogle Scholar
  24. 24.
    Baluška, F., Volkmann, D., Hlavacka, A., Mancuso, S., Barlow, P.W.: Neurobiological view of plants and their body plan. In: Communication in Plants, pp. 19–35. Springer (2006)Google Scholar
  25. 25.
    Baluška, F., Volkmann, D., Menzel, D.: Plant synapses: actin-based domains for cell-to-cell communication. Trends Plant Sci. 10(3), 106–111 (2005)CrossRefGoogle Scholar
  26. 26.
    Barlow, P.W.: The response of roots and root systems to their environmentan interpretation derived from an analysis of the hierarchical organization of plant life. Environ. Exp. Bot. 33(1), 1–10 (1993)CrossRefGoogle Scholar
  27. 27.
    Battistoni, S., Dimonte, A., Erokhin, V.: Spectrophotometric characterization of organic memristive devices. Org. Electron. 38, 79–83 (2016)CrossRefGoogle Scholar
  28. 28.
    Battistoni, S., Dimonte, A., Erokhin, V.: Organic memristor based elements for bio-inspired computing. In: Advances in Unconventional Computing, pp. 469–496. Springer (2017)Google Scholar
  29. 29.
    Bellman, R.: Dynamic programming treatment of the travelling salesman problem. J. ACM (JACM) 9(1), 61–63 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Berzina, T., Erokhin, V., Fontana, M.: Spectroscopic investigation of an electrochemically controlled conducting polymer-solid electrolyte junction. J. Appl. Phys. 101(2), 024,501 (2007)Google Scholar
  31. 31.
    Birbaum, K., Brogioli, R., Schellenberg, M., Martinoia, E., Stark, W.J., Günther, D., Limbach, L.K.: No evidence for cerium dioxide nanoparticle translocation in maize plants. Environ. Sci. Technol. 44(22), 8718–8723 (2010)CrossRefGoogle Scholar
  32. 32.
    Borghetti, J., Snidera, G.S., Kuekes, P.J., Yang, J.J., Stewart, D.R., Williams, R.S.: Memristive switches enable stateful logic operations via material implication. Nature 464(7290), 873–876 (2010)CrossRefGoogle Scholar
  33. 33.
    Brenner, E.D., Stahlberg, R., Mancuso, S., Vivanco, J., Baluška, F., Van Volkenburgh, E.: Plant neurobiology: an integrated view of plant signaling. Trends Plant Sci. 11(8), 413–419 (2006)CrossRefGoogle Scholar
  34. 34.
    Brockett, R.W.: A rational flow for the Toda lattice equations. In: Operators, Systems and Linear Algebra, pp. 33–44. Springer (1997)Google Scholar
  35. 35.
    Burbach, C., Markus, K., Zhang, Y., Schlicht, M., Baluška, F.: Photophobic behavior of maize roots. Plant Signal. Behav. 7(7), 874–878 (2012)CrossRefGoogle Scholar
  36. 36.
    Chua, L.: Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  37. 37.
    Chua, L.O., Tseng, C.W.: A memristive circuit model for p-n junction diodes. Int. J. Circuit Theory Appl. 2(4), 367–389 (1974)CrossRefGoogle Scholar
  38. 38.
    Cifarelli, A., Berzina, T., Erokhin, V.: Bio-organic memristive device: polyaniline–physarum polycephalum interface. Phys. Status Solidi (c) 12(1-2), 218–221 (2015)Google Scholar
  39. 39.
    Ciszak, M., Comparini, D., Mazzolai, B., Baluska, F., Arecchi, F.T., Vicsek, T., Mancuso, S.: Swarming behavior in plant roots. PLoS One 7(1), e29,759 (2012)Google Scholar
  40. 40.
    Costello, B.D.L., Adamatzky, A.: Experimental implementation of collision-based gates in Belousov-Zhabotinsky medium. Chaos Solitons Fractals 25(3), 535–544 (2005)Google Scholar
  41. 41.
    Costello, B.D.L., Adamatzky, A., Jahan, I., Zhang, L.: Towards constructing one-bit binary adder in excitable chemical medium. Chem. Phys. 381(1), 88–99 (2011)CrossRefGoogle Scholar
  42. 42.
    Demin, V., Erokhin, V., Emelyanov, A., Battistoni, S., Baldi, G., Iannotta, S., Kashkarov, P., Kovalchuk, M.: Hardware elementary perceptron based on polyaniline memristive devices. Org. Electron. 25, 16–20 (2015)CrossRefGoogle Scholar
  43. 43.
    DeWeese, M.R., Zador, A.: Neurobiology: efficiency measures. Nature 439(7079), 920–921 (2006)CrossRefGoogle Scholar
  44. 44.
    Dimonte, A., Battistoni, S., Erokhin, V.: Physarum in hybrid electronic devices. In: Advances in Physarum Machines, pp. 91–107. Springer (2016)Google Scholar
  45. 45.
    Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional horn formulae. J. Log. Program. 1(3), 267–284 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  46. 46.
    Emelyanov, A., Lapkin, D., Demin, V., Erokhin, V., Battistoni, S., Baldi, G., Dimonte, A., Korovin, A., Iannotta, S., Kashkarov, P., et al.: First steps towards the realization of a double layer perceptron based on organic memristive devices. AIP Adv. 6(11), 111,301 (2016)Google Scholar
  47. 47.
    Erokhin, V., Berzina, T., Camorani, P., Fontana, M.P.: Non-equilibrium electrical behaviour of polymeric electrochemical junctions. J. Phys. Condens. Matter 19(20), 205,111 (2007)Google Scholar
  48. 48.
    Erokhin, V., Berzina, T., Camorani, P., Smerieri, A., Vavoulis, D., Feng, J., Fontana, M.P.: Material memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience 1(1–2), 24–30 (2011)CrossRefGoogle Scholar
  49. 49.
    Erokhin, V., Fontana, M.P.: Electrochemically controlled polymeric device: a memristor (and more) found two years ago. arXiv preprint arXiv:0807.0333 (2008)
  50. 50.
    Erokhin, V., Howard, G.D., Adamatzky, A.: Organic memristor devices for logic elements with memory. Int. J. Bifurcat. Chaos 22(11), 1250,283 (2012)Google Scholar
  51. 51.
    Felle, H.H., Zimmermann, M.R.: Systemic signalling in barley through action potentials. Planta 226(1), 203–214 (2007)CrossRefGoogle Scholar
  52. 52.
    Fredkin, E., Toffoli, T.: Conservative logic. In: A. Adamatzky (ed.) Collision-Based Computing. Springer (2002)Google Scholar
  53. 53.
    Fromm, J., Lautner, S.: Electrical signals and their physiological significance in plants. Plant Cell Environ. 30(3), 249–257 (2007)CrossRefGoogle Scholar
  54. 54.
    Gács, P., Kurdyumov, G.L., Levin, L.A.: One-dimensional uniform arrays that wash out finite islands. Probl. Peredachi Informatsii 14(3), 92–96 (1978)Google Scholar
  55. 55.
    Gagliano, M., Mancuso, S., Robert, D.: Towards understanding plant bioacoustics. Trends Plant Sci 17(6), 323–325 (2012)CrossRefGoogle Scholar
  56. 56.
    Gagliano, M., Renton, M., Depczynski, M., Mancuso, S.: Experience teaches plants to learn faster and forget slower in environments where it matters. Oecologia 175(1), 63–72 (2014)CrossRefGoogle Scholar
  57. 57.
    Gagliano, M., Renton, M., Duvdevani, N., Timmins, M., Mancuso, S.: Acoustic and magnetic communication in plants: is it possible? Plant Signal Behav 7(10), 1346–1348 (2012)CrossRefGoogle Scholar
  58. 58.
    Gale, E., Adamatzky, A., de Lacy Costello, B.: Slime mould memristors. BioNanoScience 5(1), 1–8 (2015)Google Scholar
  59. 59.
    Gao, L., Alibart, F., Strukov, D.B.: Programmable cmos/memristor threshold logic. IEEE Trans. Nanotechnol. 12(2), 115–119 (2013)CrossRefGoogle Scholar
  60. 60.
    Geddes, L., Baker, L.: The specific resistance of biological materiala compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. 5(3), 271–293 (1967)CrossRefGoogle Scholar
  61. 61.
    Gizzie, N., Mayne, R., Patton, D., Kendrick, P., Adamatzky, A.: On hybridising lettuce seedlings with nanoparticles and the resultant effects on the organisms electrical characteristics. Biosystems 147, 28–34 (2016)CrossRefGoogle Scholar
  62. 62.
    Graham, T.L.: Flavonoid and isoflavonoid distribution in developing soybean seedling tissues and in seed and root exudates. Plant Physiol. 95(2), 594–603 (1991)CrossRefGoogle Scholar
  63. 63.
    Gunji, Y.P., Nishiyama, Y., Adamatzky, A., Simos, T.E., Psihoyios, G., Tsitouras, C., Anastassi, Z.: Robust soldier crab ball gate. Complex systems 20(2), 93 (2011)Google Scholar
  64. 64.
    Harding, S., Koutnik, J., Greff, K., Schmidhuber, J., Adamatzky, A.: Discovering Boolean gates in slime mould. arXiv preprint arXiv:1607.02168 (2016)
  65. 65.
    James, M.L., Smith, G.M., Wolford, J.C.: Analog computer simulation of engineering systems. International Textbook Company (1966)Google Scholar
  66. 66.
    Johnson, C.L.: Analog Computer Techniques. McGraw-Hill Book Company, Incorporated (1963)Google Scholar
  67. 67.
    Kalmar, L., Suranyi, J.: On the reduction of the decision problem. J. Symb. Log. 12(03), 65–73 (1947)CrossRefzbMATHGoogle Scholar
  68. 68.
    Kosta, S.P., Kosta, Y., Bhatele, M., Dubey, Y., Gaur, A., Kosta, S., Gupta, J., Patel, A., Patel, B.: Human blood liquid memristor. Int. J. Med. Eng. Inform. 3(1), 16–29 (2011)CrossRefGoogle Scholar
  69. 69.
    Kvatinsky, S., Belousov, D., Liman, S., Satat, G., Wald, N., Friedman, E.G., Kolodny, A., Weiser, U.C.: MAGIC - memristor-aided logic. IEEE Trans. Circuits Syst. 61-II(11), 895–899 (2014)Google Scholar
  70. 70.
    Kvatinsky, S., Wald, N., Satat, G., Kolodny, A., Weiser, U.C., Friedman, E.G.: Mrl—memristor ratioed logic. In: 2012 13th International Workshop on Cellular Nanoscale Networks and their Applications, pp. 1–6 (2012)Google Scholar
  71. 71.
    Lehtonen, E., Tissari, J., Poikonen, J.H., Laiho, M., Koskinen, L.: A cellular computing architecture for parallel memristive stateful logic. Microelectron. J. 45(11), 1438–1449 (2014)CrossRefGoogle Scholar
  72. 72.
    Linn, E., Rosezin, R., Tappertzhofen, S., Bttger, U., Waser, R.: Beyond von Neumann logic operations in passive crossbar arrays alongside memory operations. Nanotechnology 23(30), 305,205 (2012)Google Scholar
  73. 73.
    Lykkebø, O.R., Harding, S., Tufte, G., Miller, J.F.: MECOBO: A hardware and software platform for in materio evolution. In: International Conference on Unconventional Computation and Natural Computation, pp. 267–279. Springer (2014)Google Scholar
  74. 74.
    Lykkebø, O.R., Nichele, S., Tufte, G.: An investigation of square waves for evolution in carbon nanotubes material. In: 13th European Conference on Artificial Life (2015)Google Scholar
  75. 75.
    Mancuso, S.: Hydraulic and electrical transmission of wound-induced signals in vitis vinifera. Funct. Plant Biol. 26(1), 55–61 (1999)Google Scholar
  76. 76.
    Mancuso, S.: Seasonal dynamics of electrical impedance parameters in shoots and leaves related to rooting ability of olive (Olea europea) cuttings. Tree Physiol. 19(2), 95–101 (1999)CrossRefGoogle Scholar
  77. 77.
    Martinsen, Ø.G., Grimnes, S., Lütken, C., Johnsen, G.: Memristance in human skin. In: Journal of Physics: Conference Series, vol. 224, p. 012071. IOP Publishing (2010)Google Scholar
  78. 78.
    Masi, E., Ciszak, M., Stefano, G., Renna, L., Azzarello, E., Pandolfi, C., Mugnai, S., Baluška, F., Arecchi, F., Mancuso, S.: Spatiotemporal dynamics of the electrical network activity in the root apex. Proc. Natl. Acad. Sci. 106(10), 4048–4053 (2009)CrossRefGoogle Scholar
  79. 79.
    Massey, M., Kotsialos, A., Qaiser, F., Zeze, D., Pearson, C., Volpati, D., Bowen, L., Petty, M.: Computing with carbon nanotubes: Optimization of threshold logic gates using disordered nanotube/polymer composites. J. Appl. Phys. 117(13), 134,903 (2015)Google Scholar
  80. 80.
    Miller, J.F., Harding, S.L., Tufte, G.: Evolution-in-materio: evolving computation in materials. Evol. Intell. 7(1), 49–67 (2014)CrossRefGoogle Scholar
  81. 81.
    Mills, J.: Kirchhoff-Lukasiewicz Machines. Indiana University Web Sites Collection. (1995)Google Scholar
  82. 82.
    Mills, J.W.: The nature of the extended analog computer. Phys. D. 237(9), 1235–1256 (2008)Google Scholar
  83. 83.
    Morgan, A.J., Barrow, D.A., Adamatzky, A., Hanczyc, M.M.: Simple fluidic digital half-adder. arXiv preprint arXiv:1602.01084 (2016)
  84. 84.
    Ore, O.: Note on Hamilton circuits. Am. Math. Mon. 67(1), 55–55 (1960)Google Scholar
  85. 85.
    Papandroulidakis, G., Vourkas, I., Vasileiadis, N., Sirakoulis, G.Ch.: Boolean logic operations and computing circuits based on memristors. IEEE Trans. Circuits Syst. II Express Br. 61(12), 972–976 (2014)Google Scholar
  86. 86.
    Perel’man, M.E., Rubinstein, G.M.: Ultrasound vibrations of plant cells membranes: water lift in trees, electrical phenomena. arXiv:preprint physics/0611133 (2006)Google Scholar
  87. 87.
    Pershin, Y.V., Ventra, M.D.: Neuromorphic, digital, and quantum computation with memory circuit elements. Proc. IEEE 100(6), 2071–2080 (2012)CrossRefGoogle Scholar
  88. 88.
    Peterson, G.R.: Basic Analog Computation. Macmillan (1967)Google Scholar
  89. 89.
    Schlicht, M., Ludwig-Müller, J., Burbach, C., Volkmann, D., Baluska, F.: Indole-3-butyric acid induces lateral root formation via peroxisome-derived indole-3-acetic acid and nitric oxide. New Phytol. 200(2), 473–482 (2013)CrossRefGoogle Scholar
  90. 90.
    Semiconductor Industry Association: International Technology Roadmap for Semiconductors (ITRS). Semiconductor Industry Association (2007). http://www.itrs2.net
  91. 91.
    Soroka, W.W.: Analog Methods in Computation and Simulation. McGraw-Hill (1954)Google Scholar
  92. 92.
    Steinkellner, S., Lendzemo, V., Langer, I., Schweiger, P., Khaosaad, T., Toussaint, J.P., Vierheilig, H.: Flavonoids and strigolactones in root exudates as signals in symbiotic and pathogenic plant-fungus interactions. Molecules 12(7), 1290–1306 (2007)CrossRefGoogle Scholar
  93. 93.
    Stone, B.B., Esmon, C.A., Liscum, E.: Phototropins, other photoreceptors, and associated signaling: the lead and supporting cast in the control of plant movement responses. Curr. Top. Dev. Biol. 66, 215–238 (2005)CrossRefGoogle Scholar
  94. 94.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80–83 (2008)CrossRefGoogle Scholar
  95. 95.
    Sugiyama, A., Yazaki, K.: Root exudates of legume plants and their involvement in interactions with soil microbes. In: Secretions and exudates in biological systems, pp. 27–48. Springer (2012)Google Scholar
  96. 96.
    Tarabella, G., D’Angelo, P., Cifarelli, A., Dimonte, A., Romeo, A., Berzina, T., Erokhin, V., Iannotta, S.: A hybrid living/organic electrochemical transistor based on the Physarum polycephalum cell endowed with both sensing and memristive properties. Chem. Sci. 6(5), 2859–2868 (2015)Google Scholar
  97. 97.
    Trewavas, A.: Green plants as intelligent organisms. Trends Plant Sci. 10(9), 413–419 (2005)CrossRefGoogle Scholar
  98. 98.
    Trewavas, A.: What is plant behaviour? Plant Cell Environ. 32(6), 606–616 (2009)CrossRefGoogle Scholar
  99. 99.
    Trewavas, A.J., Baluška, F.: The ubiquity of consciousness. EMBO Rep. 12(12), 1221–1225 (2011)CrossRefGoogle Scholar
  100. 100.
    Volkov, A.G.: Electrophysiology and phototropism. In: Communication in Plants, pp. 351–367. Springer (2006)Google Scholar
  101. 101.
    Volkov, A.G., Ranatunga, D.R.A.: Plants as environmental biosensors. Plant Signal. Behav. 1(3), 105–115 (2006)CrossRefGoogle Scholar
  102. 102.
    Volkov, A.G., Tucket, C., Reedus, J., Volkova, M.I., Markin, V.S., Chua, L.: Memristors in plants. Plant Signal. Behav. 9(3), e28,152 (2014)Google Scholar
  103. 103.
    Vourkas, I., Sirakoulis, G.Ch.: Memristor-based combinational circuits: a design methodology for encoders/decoders. Microelectron. J. 45(1), 59–70 (2014)Google Scholar
  104. 104.
    Vourkas, I., Sirakoulis, G.Ch.: Emerging memristor-based logic circuit design approaches: a review. IEEE Circuits Syst. Mag. 16(3), 15–30 (2016)Google Scholar
  105. 105.
    Vourkas, I., Sirakoulis, G.Ch.: Memristor-based nanoelectronic computing circuits and architectures. In: Emergence Complexity and Computation. Springer, Cham (2016)Google Scholar
  106. 106.
    Weyrick, R.C.: Fundamentals of Analog Computers. Prentice Hall (1969)Google Scholar
  107. 107.
    Xu, W., Ding, G., Yokawa, K., Baluška, F., Li, Q.F., Liu, Y., Shi, W., Liang, J., Zhang, J.: An improved agar-plate method for studying root growth and response of Arabidopsis thaliana. Sci. Rep. 3, 1273 (2013)Google Scholar
  108. 108.
    Yokawa, K., Baluska, F.: Binary decisions in maize root behavior: Y-maze system as tool for unconventional computation in plants. IJUC 10(5–6), 381–390 (2014)Google Scholar
  109. 109.
    Yokawa, K., Kagenishi, T., Kawano, T., Mancuso, S., Baluška, F.: Illumination of arabidopsis roots induces immediate burst of ros production. Plant Signal. Behav. 6(10), 1460–1464 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Andrew Adamatzky
    • 1
    Email author
  • Simon Harding
    • 1
  • Victor Erokhin
    • 2
  • Richard Mayne
    • 1
  • Nina Gizzie
    • 1
  • Frantisek Baluška
    • 3
  • Stefano Mancuso
    • 4
  • Georgios Ch. Sirakoulis
    • 5
  1. 1.Unconventional Computing CentreBristolUK
  2. 2.CNR-IMEMParmaItaly
  3. 3.Institute of Cellular and Molecular Botany, University of BonnBonnGermany
  4. 4.International Laboratory of Plant NeurobiologyUniversity of FlorenceFirenzeItaly
  5. 5.Department of Electrical & Computer EngineeringDemocritus University of ThraceXanthiGreece

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