30-10-2002
UNDER CONSTRUCTION

Fractal structure of evolutionary trees

Figure 1. The dates of major evolutionary events of seven lineages (common evolution from life origin to viviparity, Theropod and Sauropod dinosaurs, Rodents, Equidae, Primates including Hominidae, and Echinoderms) are plotted as black points in terms of log(Tc-T), and compared with the numerical values from their corresponding log-periodic models (computed with their best-fit parameters). The adjusted critical time Tc  and scale ratio g  are indicated for each lineage. Note the deceleration of the echinoderm lineage, while all other lineages studied here show log-periodic acceleration.

References.
 

  • Nottale, L., 1997, in "Scale invariance and beyond", proceedings of Les Houches school, Ed. B. Dubrulle, F. Graner and D. Sornette, (EDP Sciences / Springer), p. 249

    •  "Scale relativity"    (PDF)
     
  • Chaline, J., Nottale, L., Grou, P., 1999, C.R. Acad. Sci. Paris, 328, IIa, 717

    •  "Is the tree of life a fractal structure ?"   (PDF)
    Réprinted in: "Points sur... Sciences de la Terre IX: évolution", (Académie des Sciences, Elsevier 2001)
     
  • Chaline J., Nottale L. et Grou P. 1999, C. R. Acad. Sci. Paris, 329, IIa, 849.

    •  Answer to the commentary of Eric Buffetaut about "Point sur... Is the tree of life a fractal structure? "
     
  • Nottale, L., Chaline, J., & Grou, P., 2000, Hachette, 379 pp.

    •  "Les arbres de l'évolution: Univers, Vie, Sociétés"    ( Book In French)
     
  • Nottale, L., Chaline, J., & Grou, P., 2001, in Fractals in Biology and Medicine, Vol III, Proceedings of Fractal 2000 Third International Symposium, Eds. G. Losa, D. Merlini, T. Nonnenmacher and E. Weibel, Birckhäuser Verlag, p. 247.

    •  "On the fractal structure of evolutionary trees"   (PDF)
     
  • Nottale, L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116

    •  "Relativité d'échelle et morphogénèse"   (PDF, In French)
     
  • Nottale, L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel, (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265.

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal"   (PDF, in French)
     
  • Cash R., Chaline, J., Nottale, L., Grou, P., 2002, C.R. Biologies  325, 585-590

    •  "Human development and log-periodic laws ".  (PDF)
     
  • Grou P., Nottale L.,Chaline J., 2002, in "Evénements rapides, instabilités, changements culturels au quaternaire", Colloquium, Aix-en-Provence, preprint (unpublished)

    •  "Evolution morphologique et culturelle humaine: l'apport des modèles fractals "   (PDF, in French)