Investigation of fractality and variation of fractal dimension in germinating seed

  • Mohanachandran Nair Sindhu Swapna
  • Sankararaman Sreejyothi
  • Sankaranarayana SankararamanEmail author
Regular Article


The fractal analysis has now been recognized as a potential mathematical tool in analyzing complex structures. The present work reports not only the fractal nature of Vigna radiata seed analyzed with the help of Field Emission Scanning Electron Microscopic images but also the variation of fractal dimension (FD) in a germinating seed. The variation of FD during germination in different media—water, salt, and diesel soot with carbon nanoparticles (CNPs)—is studied using the box-counting technique. The study is the first report of the fractality of seed. Irrespective of the media, the FD attains a maximum value on the day of germination and decreases after that. The time (T) for achieving maximum FD varies with the nature of stress. In the study, when the CNPs of diesel soot lower the T value, the salt raises the T value with respect to the control set. The Fourier Transform Infrared analysis of the seeds germinating in different media shows an increased rate of protein formation during the initial stage of germination and a steady state after that. In conjunction with the literature, the variation in the amino nitrogen, soluble nucleotide—RNA, and protein content of the seed during the initial days of germination gets reflected in its FD.



The authors are thankful to Dr. K. V. Dominic, Professor of English (Retired) and Editor-in-Chief, Writers Editors Critics (WEC) for the support given in English language editing.

Author contributions

All authors contributed equally to this manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

Research involving human participants

This article does not contain any studies with human participants performed by any of the author.


  1. 1.
    M.S. Swapna, H.V.S. Devi, V. Raj, S. Sankararaman, Eur. Phys. J. Plus 133, 106 (2018)CrossRefGoogle Scholar
  2. 2.
    K. Falconer, Fractals: a very short introduction (Oxford University Press, United Kingdom, 2013)zbMATHCrossRefGoogle Scholar
  3. 3.
    V. Raj, M.S. Swapna, S. Soumya, S. Sankararaman, Indian J. Phys. 5, 115504 (2019)Google Scholar
  4. 4.
    E.M. Miedziejko, Acta Agrophys. 7, 141 (2006)Google Scholar
  5. 5.
    B.B. Mandelbrot, The fractal geometry of nature (WH freeman, New York, 1983)CrossRefGoogle Scholar
  6. 6.
    B.B. Mandelbrot, Proc. Natl. Acad. Sci. 72, 3825 (1975)ADSCrossRefGoogle Scholar
  7. 7.
    B.J. West, A.L. Goldberger, Am. Sci. 75, 354 (1987)ADSGoogle Scholar
  8. 8.
    H.M. Hastings, G. Sugihara, Fractals. A user's guide for the natural sciences (Oxford University Press, Oxford, 1993)zbMATHGoogle Scholar
  9. 9.
    N.C. Kenkel, D.J. Walker, Coenoses 11, 77 (1996)Google Scholar
  10. 10.
    P.S. Addison, Fractals and chaos—an illustrated course (Institute of Physics Publishing, Bristol, 1997)zbMATHCrossRefGoogle Scholar
  11. 11.
    J. Gleick, Chaos, making a new science (Penguin Books, New York, 1987)zbMATHGoogle Scholar
  12. 12.
    G. Captur, A.L. Karperien, A.D. Hughes, D.P. Francis, J.C. Moon, Nat. Rev. Cardiol. 14, 56 (2017)CrossRefGoogle Scholar
  13. 13.
    M.S. Swapna, S.S. Shinker, S. Suresh, S. Sankararaman, Biomed. Mater. Eng. 29, 787 (2018)Google Scholar
  14. 14.
    B. Klinkenberg, Math. Geol. 26, 23 (1994)CrossRefGoogle Scholar
  15. 15.
    H.E. Schepers, J.H.G.M. van Beek, J.B. Bassingthwaighte, IEEE Eng. Med. Biol. Mag. 11, 57 (1992)CrossRefGoogle Scholar
  16. 16.
    S. Soumya, M.S. Swapna, V. Raj, V.P.M. Pillai, S. Sankararaman, Eur. Phys. J. Plus 132, 551 (2017)CrossRefGoogle Scholar
  17. 17.
    W. Deering, B.J. West, I.E.E.E. Eng, Med. Biol. Mag. 11, 40 (1992)Google Scholar
  18. 18.
    N.C. Kenkel, D.J. Walker, Abstr. Bot. 17, 53 (1993)Google Scholar
  19. 19.
    G. Losa, Fract. Geom. Nonlinear Anal. Med. Biol. 1, 11 (2015)Google Scholar
  20. 20.
    G. Sugihara, R.M. May, Trends Ecol. Evol. 5, 79 (1990)CrossRefGoogle Scholar
  21. 21.
    B. Hao, H.-C. Lee, S. Zhang, Chaos. Solitons & Fractals 11, 825 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    H.E. Stanley, Phys. A Stat. Mech. Appl. 186, 1 (1992)CrossRefGoogle Scholar
  23. 23.
    M. Takahashi, J. Theor. Biol. 141, 117 (1989)CrossRefGoogle Scholar
  24. 24.
    T.G. Smith Jr., W.B. Marks, G.D. Lange, W.H. Sheriff Jr., E.A. Neale, J. Neurosci. Methods 27, 173 (1989)CrossRefGoogle Scholar
  25. 25.
    M. Lewis, D.C. Rees, Science 230, 1163 (1985)ADSCrossRefGoogle Scholar
  26. 26.
    L.S. Liebovitch, J. Fischbarg, J.P. Koniarek, Math. Biosci. 84, 37 (1987)MathSciNetCrossRefGoogle Scholar
  27. 27.
    H. A. do Prado, A.J.B. Luiz, H.C. Filho, Computational methods for agricultural research: advances and applications. Information Science Reference, Hershey (2011).Google Scholar
  28. 28.
    N.C. Kenkel, A.J. Irwin, Abstr. Bot. 79, 77–100 (1994)Google Scholar
  29. 29.
    S.G. Chen, R. Ceulemans, I. Impens, For. Ecol. Manage. 69, 97 (1994)CrossRefGoogle Scholar
  30. 30.
    E. Perfect, B.D. Kay, Soil Sci. Soc. Am. J. 55, 1552 (1991)ADSCrossRefGoogle Scholar
  31. 31.
    E. Perfect, B.D. Kay, V. Rasiah, Soil Sci. Soc. Am. J. 57, 896 (1993)ADSCrossRefGoogle Scholar
  32. 32.
    O.M. Bruno, R. De Oliveira Plotze, M. Falvo, M. De Castro, Inf. Sci. 178, 2722 (2008)CrossRefGoogle Scholar
  33. 33.
    K.W. Ketipearachchi, J. Tatsumi, Plant Prod. Sci. 3, 289 (2000)CrossRefGoogle Scholar
  34. 34.
    M.K. Biswas, T. Ghose, S. Guha, P.K. Biswas, Pattern Recognit. Lett. 19, 309 (1998)CrossRefGoogle Scholar
  35. 35.
    N. Buchman, K. Cuddington, Environ. Entomol. 38, 962 (2009)CrossRefGoogle Scholar
  36. 36.
    P.E. Waggoner, J.-Y. Parlange, Plant Physiol. 57, 153 (1976)CrossRefGoogle Scholar
  37. 37.
    A. Kamal, Physiological and biochemical responses of medicinally important nigella sativa plant in different phases of germination (Integral University, Lucknow, 2013)Google Scholar
  38. 38.
    K. Weitbrecht, K. Müller, G. Leubner-Metzger, J. Exp. Bot. 62, 3289 (2011)CrossRefGoogle Scholar
  39. 39.
    T. Bareke, Adv. Plants Agric. Res. 8, 336 (2018)Google Scholar
  40. 40.
    M.A.O. Santos, A.D.L.C. Novembre, J. Marcos-Filho, Seed Sci. Technol. 35, 213 (2007)CrossRefGoogle Scholar
  41. 41.
    E.A. Hunter, C.A. Glasbey, R.E.L. Naylor, J. Agric. Sci. 102, 207 (1984)CrossRefGoogle Scholar
  42. 42.
    V.D. Rajput, T. Minkina, S. Suskova, S. Mandzhieva, V. Tsitsuashvili, V. Chapligin, A. Fedorenko, Bionanoscience 8, 36 (2018)CrossRefGoogle Scholar
  43. 43.
    P. Moni, M. Wilhelm, K. Rezwan, RSC Adv. 7, 37559 (2017)CrossRefGoogle Scholar
  44. 44.
    M. Khodakovskaya, E. Dervishi, M. Mahmood, Y. Xu, Z. Li, F. Watanabe, A.S. Biris, ACS Nano 3, 3221 (2009)CrossRefGoogle Scholar
  45. 45.
    M. Iqbal, M. Shafiq, S. Zaidi, M. Athar, Glob. J. Environ. Sci. Manag. 1, 283 (2015)Google Scholar
  46. 46.
    M.S. Swapna, V. Raj, H.V.S. Devi, S. Sankararaman, Photochem. Photobiol. Sci. 18, 1382 (2019)CrossRefGoogle Scholar
  47. 47.
    M.S. Swapna, S. Sankararaman, J. Mater. Sci. Nanotechnol. 5, 104 (2017)Google Scholar
  48. 48.
    M.S. Swapna, S. Sankararaman, Int. Nano Lett. 9, 221 (2019)CrossRefGoogle Scholar
  49. 49.
    P.S. Addison, The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance (CRC, Oxford, 2017)zbMATHGoogle Scholar
  50. 50.
    P.J.M. Pelgrom, R.M. Boom, M.A.I. Schutyser, Food Bioprocess Technol. 8, 1495 (2015)CrossRefGoogle Scholar
  51. 51.
    L.L. De Azevedo Bittencourt, C. Pedrosa, V.P. De Sousa, A.P.T. Pierucci, M. Citelli, Plant Foods Hum. Nutr. 68, 333 (2013)CrossRefGoogle Scholar
  52. 52.
    M.V. Khodakovskaya, K. De Silva, A.S. Biris, E. Dervishi, H. Villagarcia, ACS Nano 6, 2128 (2012)CrossRefGoogle Scholar
  53. 53.
    K. Pandey, M.H. Lahiani, V.K. Hicks, M.K. Hudson, M.J. Green, M. Khodakovskaya, PLoS ONE 13, e0202274 (2018)CrossRefGoogle Scholar
  54. 54.
    R. Nair, M.S. Mohamed, W. Gao, T. Maekawa, Y. Yoshida, P.M. Ajayan, D.S. Kumar, J. Nanosci. Nanotechnol. 12, 2212 (2012)CrossRefGoogle Scholar
  55. 55.
    M.S. Swapna, S. Sankararaman, Nano-Struct. Nano-Obj. 19, 100375 (2019)CrossRefGoogle Scholar
  56. 56.
    M.S. Swapna, S. Sankararaman, J. Fluoresc. 28, 543 (2018)CrossRefGoogle Scholar
  57. 57.
    E. Xu, M. Chen, H. He, C. Zhan, Y. Cheng, H. Zhang, Z. Wang, Front. Plant Sci. 7, 2006 (2017)Google Scholar
  58. 58.
    S.E.B. Gould, D.A. Rees, J. Sci. Food Agric. 16, 702 (1965)CrossRefGoogle Scholar
  59. 59.
    A.M.S.A. Qados, J. Saudi Soc. Agric. Sci. 10, 7 (2011)Google Scholar
  60. 60.
    H. Zhang, L.J. Irving, Y. Tian, D. Zhou, South Afr. J. Bot. 78, 203 (2012)CrossRefGoogle Scholar
  61. 61.
    P. Neumann, Plant. Cell Environ. 20, 1193 (1997)CrossRefGoogle Scholar
  62. 62.
    R. Lahlali, Y. Jiang, S. Kumar, C. Karunakaran, X. Liu, F. Borondics, E. Hallin, R. Bueckert, Front Plant Sci. 5, 747 (2014)CrossRefGoogle Scholar
  63. 63.
    L. Beevers, F.S. Guernsey, Plant Physiol. 41, 1455 (1966)CrossRefGoogle Scholar
  64. 64.
    B.R. Wood, Chem. Soc. Rev. 45, 1980 (2016)CrossRefGoogle Scholar
  65. 65.
    G.R. Barker, T. Douglas, Nature 188, 943 (1960)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of OptoelectronicsUniversity of KeralaTrivandrumIndia
  2. 2. Department of Nanoscience and NanotechnologyUniversity of KeralaTrivandrumIndia
  3. 3.Department of Electronics and Communication EngineeringMuthoot Institute of Technology and ScienceCochinIndia

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