The Book of L pp 431-444 | Cite as

Development, Growth and Time

  • Paul M. B. Vitãnyi


We propose a simple mathematical model for filamentous growth and development. The new model relates stereotype elemental (cellular) behavior to empirically observed overall growth curves. As examples we obtain the sigmoidal growth curves. Basic is the separation of subjective or physiological time of the organism from objective or absolute time and the relation between them. The underlying philosophy is related to Lindenmayer’s developmental model.


Growth Function Physical Time Division Rate Division Pattern Physiological Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Erickson, R.O. and K.B. Sax, “Elemental growth rate of the primary root of Zea maysProc. American Philosophical Society, vol. 100, pp.487–498, 1956.Google Scholar
  2. [2]
    Erickson, R.O. and K.B. Sax, “Rates of cell division and cell elongation in the growth of the primary root of Zea mays” Proc. American Philosophical Society, vol. 100, pp.499–514, 1956.Google Scholar
  3. [3]
    Erickson, R.O., Private communication, 1975.Google Scholar
  4. [4]
    Herman, G.T. and G. Rozenberg, Developmental Systems and Languages. Amsterdam:North-Holland, 1975.Google Scholar
  5. [5]
    Herman, G.T. and P.M.B. Vitányi, “Growth functions associated with biological development,” American Mathematical Monthly, vol. 83, pp.1–15, 1976.MATHCrossRefGoogle Scholar
  6. [6]
    Lindenmayer, A., “Mathematical models for cellular interactions in development, Parts I & II,” Journal of Theoretical Biology, vol. 18, pp.280–299&300-315, 1968.CrossRefGoogle Scholar
  7. [7]
    Lück, H.B., “Sur la traduction morphogénétique de la cinétique cellulaire pendant la croissance des entre-noeuds de Tradeacantia Flumensis Vel.,” Bull, de la Société Botanique de France, pp.220–225, 1966.Google Scholar
  8. [8]
    Lück, H.B., Private communication, 1975.Google Scholar
  9. [9]
    Lück, H.B. and J. Lück, “Cell number and cell size in filamentous organisms in relation to ancestrally and positionally dependant generation times,” pp. 109–124 in Automata, Languages, Development, ed. A. Lindenmayer and G. Rozenberg, North-Holland, Amsterdam (1976).Google Scholar
  10. [10]
    Lück, H.B., Private communication, 1977.Google Scholar
  11. [11]
    Lück, H.B., Private communication, 1977.Google Scholar
  12. [12]
    Medawar, P.B., “Size, shape and age,” in Essays on Growth and Form, ed. W.E. Le Gros Clark and P.B. Medawar, Clarendon Press, Oxford (1945).Google Scholar
  13. [13]
    Sandland, R.L., “Mathematics and the growth of organisms — Some historical impressions,” The Mathematical Scientist, vol. 8, pp.11–30, 1983.MathSciNetMATHGoogle Scholar
  14. [14]
    Thompson, D’A. W., On Growth and Form, 2nd Edition. Cambridge University Press, 1942.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Paul M. B. Vitãnyi
    • 1
  1. 1.Centre for Mathematics & Computer Science (CWI)AmsterdamThe Netherlands

Personalised recommendations